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Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday

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A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (28 February 2023) | Viewed by 26328

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Special Issue Editors

Prof. Dr. Sevtap Sümer Eker

E-Mail Website
Guest Editor

Department of Mathematics, Faculty of Science, Dicle University, 21280 Diyarbakır, Turkey
Interests: univalent functions; bi-univalent functions; starlike; hankel determinant

Prof. Dr. Juan J. Nieto

E-Mail Website
Guest Editor

Department of Statistics, Mathematical Analysis and Optimization, CITMAga, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain
Interests: nonlinear differential equations; fractional models; biomedical applications; digital twins
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recognition of his significant contributions in many scientific fields, this Special Issue is dedicated to Professor Hari Mohan Srivastava on the occasion of his 82nd birthday on 05 July 2022. Professor Srivastava is one of the most distinguished and globally recognized mathematical scientists.

Currently, Professor Srivastava holds the position of Professor Emeritus in the Department of Mathematics and Statistics at the University of Victoria in Canada, having joined the faculty there in 1969. Professor Srivastava has held (and continues to hold) numerous Visiting and Chair Professorships at many universities and research institutes in many different parts of the world. Having received several D.Sc. (honoris causa) degrees as well as honorary memberships and fellowships of many scientific academies and scientific societies around the world, he is also actively associated editorially with numerous international scientific research journals as an Honorary or Advisory Editor or as an Editorial Board Member. He has also edited (and is currently editing) many Special Issues of scientific research journals as Guest Editor, including the MDPI journals Axioms, Mathematics, Symmetry, Entropy, Applied Sciences, and Journal of Risk and Financial Management; the Elsevier journals Journal of Computational and Applied Mathematics, Applied Mathematics and Computation, Chaos, Solitons and Fractals, Alexandria Engineering Journal, and Journal of King Saud University – Science; the Wiley journal Mathematical Methods in the Applied Sciences; and many other scientific research journals. He has been a Clarivate Analytics [Thomson Reuters] (Web of Science) Highly-Cited Researcher since 2015. He is also listed and ranked Sixth Place in General Mathematics among the Top 2% Scientists in the World 2021 (Published by Stanford University in U.S.A.).

Professor Srivastava’s research interests include several areas of pure and applied mathematical sciences, such as real and complex analysis, fractional calculus and its applications, integral equations and integral transforms, higher transcendental functions and their applications, q-series and q-polynomials, analytic number theory, analytic and geometric inequalities, differential and difference equations, probability and statistics, and inventory modeling and optimization. He has published 45 books, monographs, and edited volumes; 36 book (and encyclopedia) chapters; 48 papers in international conference proceedings; and more than 1400 articles in various peer-reviewed international scientific research journals; as well as forewords and prefaces to many books and journals.

Further details about Professor Srivastava’s professional achievements and scholarly accomplishments, as well as the honors, awards and distinctions accorded to him, can be found at the following website: http://www.math.uvic.ca/~harimsri/.

Professor Hari Mohan Srivastava is an amazing man and a leading mathematician. With his pioneer vision and crucial contributions to the development of mathematical analysis, Professor Srivastava has been a role model and inspiration for every mathematician and countless others whose lives he has touched. Professor Srivastava is a very kind, loving, and helpful person to everyone.

Finally, we wish him a healthy and happy long life with his esteemed wife Professor Rekha Srivastava and his children and grandchildren. May he continue to guide, encourage, and enlighten researchers in mathematical and allied sciences for decades to come.

We look forward to receiving your contributions to this Special Issue dedicated to Professor Hari Mohan Srivastava.

Prof. Dr. Sevtap Sümer Eker
Prof. Dr. Juan J. Nieto
Guest Editors

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

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Keywords

functional analysis
geometric function theory
functions of complex variables
differential subordination and superordination
harmonic functions
special functions
fractional calculus
quantum calculus
fractional differential equations
fractional models
digital twins
mathematical methods in quantum information

Published Papers (22 papers)

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Research

13 pages, 2587 KiB

Open AccessArticle

Quantum Control of a Nonlinear Time-Dependent Interaction of a Damped Three-Level Atom

by Sameh Korashy and Mahmoud Abdel-Aty

Axioms 2023, 12(6), 552; https://doi.org/10.3390/axioms12060552 - 04 Jun 2023

Viewed by 909

Abstract

We investigate some new aspects of the nonlinear interaction between a three-level

Ξ

We investigate some new aspects of the nonlinear interaction between a three-level

Ξ

-type atom and bimodal field. The photon-assisted atomic phase damping, detuning parameter, Kerr nonlinearity and the time-dependent coupling have been considered. The general solution has been obtained by using the Schrődinger equation when the atom and the field are initially prepared in the excited state and coherent state, respectively. The atomic population inversion and concurrence are discussed. It is shown that the time-dependent coupling parameter and the detuning parameter can be considered as quantum controller parameters of the atomic population inversion and quantum entanglement in the considered model. Full article

(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)

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30 pages, 457 KiB

Open AccessArticle

Infinite Series and Logarithmic Integrals Associated to Differentiation with Respect to Parameters of the Whittaker W_κ,μ(x) Function II

by Alexander Apelblat and Juan Luis González-Santander

Axioms 2023, 12(4), 382; https://doi.org/10.3390/axioms12040382 - 16 Apr 2023

Viewed by 988

Abstract

In the first part of this investigation, we considered the parameter differentiation of the Whittaker function

M_{κ, μ} (x)

. In this second part, first derivatives with respect to the parameters of the Whittaker function

W_{κ, μ} (x)

are [...] Read more.

In the first part of this investigation, we considered the parameter differentiation of the Whittaker function

M_{κ, μ} (x)

. In this second part, first derivatives with respect to the parameters of the Whittaker function

W_{κ, μ} (x)

are calculated. Using the confluent hypergeometric function, these derivatives can be expressed as infinite sums of quotients of the digamma and gamma functions. Furthermore, it is possible to obtain these parameter derivatives in terms of infinite integrals, with integrands containing elementary functions (products of algebraic, exponential, and logarithmic functions), from the integral representation of

W_{κ, μ} (x)

. These infinite sums and integrals can be expressed in closed form for particular values of the parameters. Finally, an integral representation of the integral Whittaker function

{wi}_{κ, μ} (x)

and its derivative with respect to

κ

, as well as some reduction formulas for the integral Whittaker functions

{Wi}_{κ, μ} (x)

and

{wi}_{κ, μ} (x)

, are calculated. Full article

(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)

29 pages, 433 KiB

Open AccessArticle

Infinite Series and Logarithmic Integrals Associated to Differentiation with Respect to Parameters of the Whittaker M_κ_,_μ(x) Function I

by Alexander Apelblat and Juan Luis González-Santander

Axioms 2023, 12(4), 381; https://doi.org/10.3390/axioms12040381 - 16 Apr 2023

Viewed by 1036

Abstract

In this paper, first derivatives of the Whittaker function

M_{κ, μ} (x)

are calculated with respect to the parameters. Using the confluent hypergeometric function, these derivarives can be expressed as infinite sums of quotients of the digamma and gamma functions. Moreover, [...] Read more.

In this paper, first derivatives of the Whittaker function

M_{κ, μ} (x)

M_{κ, μ} (x)

it is possible to obtain these parameter derivatives in terms of finite and infinite integrals with integrands containing elementary functions (products of algebraic, exponential, and logarithmic functions). These infinite sums and integrals can be expressed in closed form for particular values of the parameters. For this purpose, we have obtained the parameter derivative of the incomplete gamma function in closed form. As an application, reduction formulas for parameter derivatives of the confluent hypergeometric function are derived, along with finite and infinite integrals containing products of algebraic, exponential, logarithmic, and Bessel functions. Finally, reduction formulas for the Whittaker functions

M_{κ, μ} (x)

and integral Whittaker functions

{Mi}_{κ, μ} (x)

and

{mi}_{κ, μ} (x)

are calculated. Full article

(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)

12 pages, 303 KiB

Open AccessArticle

New Generalization of Geodesic Convex Function

by Ohud Bulayhan Almutairi and Wedad Saleh

Axioms 2023, 12(4), 319; https://doi.org/10.3390/axioms12040319 - 23 Mar 2023

Cited by 1 | Viewed by 770

Abstract

As a generalization of a geodesic function, this paper introduces the notion of the geodesic

φ_{E}

-convex function. Some properties of the

φ_{E}

-convex function and geodesic

φ_{E}

-convex function are established. The concepts of a geodesic

φ_{E}

-convex [...] Read more.

As a generalization of a geodesic function, this paper introduces the notion of the geodesic

φ_{E}

-convex function. Some properties of the

φ_{E}

-convex function and geodesic

φ_{E}

-convex function are established. The concepts of a geodesic

φ_{E}

-convex set and

φ_{E}

-epigraph are also given. The characterization of geodesic

φ_{E}

-convex functions in terms of their

φ_{E}

-epigraphs, are also obtained. Full article

(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)

17 pages, 350 KiB

Open AccessArticle

Coefficient Bounds for a Family of s-Fold Symmetric Bi-Univalent Functions

by Isra Al-shbeil, Nazar Khan, Fairouz Tchier, Qin Xin, Sarfraz Nawaz Malik and Shahid Khan

Axioms 2023, 12(4), 317; https://doi.org/10.3390/axioms12040317 - 23 Mar 2023

Cited by 8 | Viewed by 990

Abstract

We present a new family of s-fold symmetrical bi-univalent functions in the open unit disc in this work. We provide estimates for the first two Taylor–Maclaurin series coefficients for these functions. Furthermore, we define the Salagean differential operator and discuss various applications of our main findings using it. A few new and well-known corollaries are studied in order to show the connection between recent and earlier work. Full article

(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)

11 pages, 282 KiB

Open AccessArticle

Some Subordination Results Defined by Using the Symmetric q-Differential Operator for Multivalent Functions

by Saima Noor, Sa’ud Al-Sa’di and Saqib Hussain

Axioms 2023, 12(3), 313; https://doi.org/10.3390/axioms12030313 - 22 Mar 2023

Cited by 1 | Viewed by 832

Abstract

In this article, we use the concept of symmetric q-calculus and convolution in order to define a symmetric q-differential operator for multivalent functions. This operator is an extension of the classical Ruscheweyh differential operator. By using the technique of differential subordination, [...] Read more.

(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)

15 pages, 307 KiB

Open AccessArticle

Strong and Δ-Convergence Fixed-Point Theorems Using Noor Iterations

by Asifa Tassaddiq, Shazia Kanwal, Farha Lakhani and Rekha Srivastava

Axioms 2023, 12(3), 271; https://doi.org/10.3390/axioms12030271 - 06 Mar 2023

Cited by 1 | Viewed by 1024

Abstract

A wide range of new research articles in artificial intelligence, logic programming, and other applied sciences are based on fixed-point theorems. The aim of this article is to present an approximation method for finding the fixed point of generalized Suzuki nonexpansive mappings on [...] Read more.

Δ

-convergence theorems are proved using the Noor iterative process for generalized Suzuki nonexpansive mappings (GSNM) on uniform convex hyperbolic spaces. Due to the richness of uniform convex hyperbolic spaces, the results of this paper can be used as an extension and generalization of many famous results in Banach spaces together with

C A T (0)

spaces. Full article

(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)

10 pages, 307 KiB

Open AccessArticle

Initial Coefficients Estimates and Fekete–Szegö Inequality Problem for a General Subclass of Bi-Univalent Functions Defined by Subordination

by Mohamed Illafe, Feras Yousef, Maisarah Haji Mohd and Shamani Supramaniam

Axioms 2023, 12(3), 235; https://doi.org/10.3390/axioms12030235 - 23 Feb 2023

Cited by 7 | Viewed by 1027

Abstract

In the present work, we aim to introduce and investigate a novel comprehensive subclass of normalized analytic bi-univalent functions involving Gegenbauer polynomials and the zero-truncated Poisson distribution. For functions in the aforementioned class, we find upper estimates of the second and third Taylor–Maclaurin coefficients, and then we solve the Fekete–Szegö functional problem. Moreover, by setting the values of the parameters included in our main results, we obtain several links to some of the earlier known findings. Full article

(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)

13 pages, 7640 KiB

Open AccessArticle

Approximating the Moments of Generalized Gaussian Distributions via Bell’s Polynomials

by Diego Caratelli, Ruben Sabbadini and Paolo Emilio Ricci

Axioms 2023, 12(2), 206; https://doi.org/10.3390/axioms12020206 - 15 Feb 2023

Viewed by 1144

Abstract

Bell’s polynomials are used in many different fields of mathematics, ranging from number theory to operator theory. This paper shows a relevant application in probability theory aimed at computing the moments of generalized Gaussian distributions. To this end, a table containing the first values of the complete Bell’s polynomials is provided. Furthermore, a dedicated code for approximating the moments of the general distributions in terms of complete Bell’s polynomials is detailed. Several test cases concerning different nested functions are discussed. Full article

(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)

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12 pages, 337 KiB

Open AccessArticle

A New Subclass of Bi-Univalent Functions Defined by a Certain Integral Operator

by Daniel Breaz, Halit Orhan, Luminiţa-Ioana Cotîrlă and Hava Arıkan

Axioms 2023, 12(2), 172; https://doi.org/10.3390/axioms12020172 - 08 Feb 2023

Cited by 1 | Viewed by 1409

Abstract

We introduce a comprehensive subfamily of analytic and bi-univalent functions in this study using Horadam polynomials and the q-analog of the Noor integral operator. We establish upper bounds for the absolute values of the second and the third coefficients and the Fekete–Szegö [...] Read more.

(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)

16 pages, 273 KiB

Open AccessArticle

Some Properties for Subordinations of Analytic Functions

by Hatun Özlem Güney, Daniel Breaz and Shigeyoshi Owa

Axioms 2023, 12(2), 131; https://doi.org/10.3390/axioms12020131 - 28 Jan 2023

Cited by 2 | Viewed by 934

Abstract

Let the class of functions of

f (z)

of the form

f (z) = z + \sum_{k = 2}^{\infty} a_{k} z^{k}

, which are denoted by

A

and called analytic functions in the open-unit disk. [...] Read more.

Let the class of functions of

f (z)

of the form

f (z) = z + \sum_{k = 2}^{\infty} a_{k} z^{k}

, which are denoted by

A

and called analytic functions in the open-unit disk. There are many interesting properties of the functions

f (z)

in the class

A

concerning the subordinations. Applying the three lemmas for

f (z) \in A

provided by Miller and Mocanu and by Nunokawa, we consider many interesting properties of

f (z) \in A

with subordinations. Furthermore, we provide simple examples for our results. We think it is very important to consider examples of the results. Full article

(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)

17 pages, 321 KiB

Open AccessArticle

Some Local Fractional Inequalities Involving Fractal Sets via Generalized Exponential (s,m)-Convexity

by Wedad Saleh and Adem Kılıçman

Axioms 2023, 12(2), 106; https://doi.org/10.3390/axioms12020106 - 19 Jan 2023

Cited by 2 | Viewed by 861

Abstract

Research in this paper aims to explore the concept of generalized exponentially (

s, m

)-convex functions, and to determine some properties of these functions. In addition, we look at some interactions between generalized exponentially (

s, m

)-convex functions and [...] Read more.

Research in this paper aims to explore the concept of generalized exponentially (

s, m

)-convex functions, and to determine some properties of these functions. In addition, we look at some interactions between generalized exponentially (

s, m

)-convex functions and local fractional integrals. The properties of the generalized new special cases of (

s, m

)-convex functions, s-convex functions, and also generalized m-convex functions are impressive. We derive some inequalities of Hadamard’s type for generalized exponentially (

s, m

)-convex functions, and give applications in probability density functions and generalized special methods to attest to the applicability and efficiency of the method under consideration. Full article

(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)

8 pages, 238 KiB

Open AccessArticle

On the Strong Starlikeness of the Bernardi Transform

by Zahra Orouji, Ali Ebadian and Nak Eun Cho

Axioms 2023, 12(1), 91; https://doi.org/10.3390/axioms12010091 - 16 Jan 2023

Viewed by 1046

Abstract

Many papers concern both the starlikeness and the convexity of Bernardi integral operator. Using the Nunokawa’s Lemma, we want to determine conditions for the strong starlikeness of the Bernardi transform of normalized analytic functions g, such that [...] Read more.

| arg {g^{'} (z)} | < \frac{α π}{2}

in the open unit disk

Δ

where

0 < α < 2

. Our results include the results of Mocanu, Nunokawa and others on the Libera transform. Full article

(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)

15 pages, 292 KiB

Open AccessArticle

Subclasses of Uniformly Convex Functions with Negative Coefficients Based on Deniz–Özkan Differential Operator

by Erhan Deniz, Yücel Özkan and Luminiţa-Ioana Cotîrlă

Axioms 2022, 11(12), 731; https://doi.org/10.3390/axioms11120731 - 14 Dec 2022

Viewed by 984

Abstract

We introduce in this paper a new family of uniformly convex functions related to the Deniz–Özkan differential operator. By using this family of functions with a negative coefficient, we obtain coefficient estimates, the radius of starlikeness, convexity, and close-to-convexity, and we find their [...] Read more.

(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)

16 pages, 840 KiB

Open AccessArticle

Parameterized Quantum Fractional Integral Inequalities Defined by Using n-Polynomial Convex Functions

by Rozana Liko, Hari Mohan Srivastava, Pshtiwan Othman Mohammed, Artion Kashuri, Eman Al-Sarairah, Soubhagya Kumar Sahoo and Mohamed S. Soliman

Axioms 2022, 11(12), 727; https://doi.org/10.3390/axioms11120727 - 13 Dec 2022

Cited by 2 | Viewed by 1059

Abstract

Convexity performs the appropriate role in the theoretical study of inequalities according to the nature and behaviour. There is a strong relation between symmetry and convexity. In this article, we consider a new parameterized quantum fractional integral identity. Following that, our main results are established, which consist of some integral inequalities of Ostrowski and midpoint type pertaining to n-polynomial convex functions. From our main results, we discuss in detail several special cases. Finally, an example and an application to special means of positive real numbers are presented to support our theoretical results. Full article

(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)

12 pages, 342 KiB

Open AccessArticle

Some Properties of Bazilevič Functions Involving Srivastava–Tomovski Operator

by Daniel Breaz, Kadhavoor R. Karthikeyan, Elangho Umadevi and Alagiriswamy Senguttuvan

Axioms 2022, 11(12), 687; https://doi.org/10.3390/axioms11120687 - 30 Nov 2022

Cited by 6 | Viewed by 1084

Abstract

We introduce a new class of Bazilevič functions involving the Srivastava–Tomovski generalization of the Mittag-Leffler function. The family of functions introduced here is superordinated by a conic domain, which is impacted by the Janowski function. We obtain coefficient estimates and subordination conditions for [...] Read more.

(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)

9 pages, 284 KiB

Open AccessArticle

An Application of Rabotnov Functions on Certain Subclasses of Bi-Univalent Functions

by Ala Amourah, Ibtisam Aldawish, Khadeejah Rasheed Alhindi and Basem Aref Frasin

Axioms 2022, 11(12), 680; https://doi.org/10.3390/axioms11120680 - 28 Nov 2022

Cited by 5 | Viewed by 1092

Abstract

In this study, a new class

R_{Σ}^{μ} (x, γ, α, δ, β)

of bi-univalent functions studied by means of Gegenbauer polynomials (GP) with Rabotnov functions is introduced. The coefficient of the Taylor coefficients

|a_{2}|

[...] Read more.

In this study, a new class

R_{Σ}^{μ} (x, γ, α, δ, β)

of bi-univalent functions studied by means of Gegenbauer polynomials (GP) with Rabotnov functions is introduced. The coefficient of the Taylor coefficients

|a_{2}|

and

|a_{3}|

and Fekete-Szegö problems for functions belonging to

R_{Σ}^{μ} (x, γ, α, δ, β)

have been derived as well. Furthermore, a variety of new results will appear by considering the parameters in the main results. Full article

(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)

9 pages, 293 KiB

Open AccessArticle

New Subclasses of Bi-Univalent Functions with Respect to the Symmetric Points Defined by Bernoulli Polynomials

by Mucahit Buyankara, Murat Çağlar and Luminiţa-Ioana Cotîrlă

Axioms 2022, 11(11), 652; https://doi.org/10.3390/axioms11110652 - 17 Nov 2022

Cited by 9 | Viewed by 1550

Abstract

In this paper, we introduce and investigate new subclasses of bi-univalent functions with respect to the symmetric points in

U = \{z \in C : |z| < 1\}

defined by Bernoulli polynomials. We obtain upper bounds for Taylor–Maclaurin coefficients

|a_{2}|,

[...] Read more.

In this paper, we introduce and investigate new subclasses of bi-univalent functions with respect to the symmetric points in

U = \{z \in C : |z| < 1\}

defined by Bernoulli polynomials. We obtain upper bounds for Taylor–Maclaurin coefficients

|a_{2}|,

|a_{3}|

and Fekete–Szegö inequalities

|a_{3} - μ a_{2}^{2}|

for these new subclasses. Full article

(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)

10 pages, 268 KiB

Open AccessArticle

Some Inequalities for Certain p-Valent Functions Connected with the Combination Binomial Series and Confluent Hypergeometric Function

by Sheza M. El-Deeb and Adriana Cătaş

Axioms 2022, 11(11), 631; https://doi.org/10.3390/axioms11110631 - 10 Nov 2022

Cited by 2 | Viewed by 1029

Abstract

The present paper deals with a new differential operator denoted by

F_{p, t}^{δ, n, b, c, m, β}

, whose certain properties are deduced by using well-known earlier studies regarding differential inequalities and the Caratheodory [...] Read more.

The present paper deals with a new differential operator denoted by

F_{p, t}^{δ, n, b, c, m, β}

, whose certain properties are deduced by using well-known earlier studies regarding differential inequalities and the Caratheodory function. The new introduced operator is defined by making use of a linear combination of the binomial series and confluent hypergeometric function. In addition, by using special values of the parameters, we establish certain results concretized in specific corollaries, which provide useful inequalities. Studying these properties by using various types of operators is a technique that is widely used. Full article

(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)

12 pages, 331 KiB

Open AccessArticle

Fekete-Szegö Inequalities for Some Certain Subclass of Analytic Functions Defined with Ruscheweyh Derivative Operator

by Halit Orhan and Luminiţa-Ioana Cotîrlă

Axioms 2022, 11(10), 560; https://doi.org/10.3390/axioms11100560 - 15 Oct 2022

Cited by 3 | Viewed by 1280

Abstract

In our present investigation, we introduce and study some new subclasses of analytic functions associated with Ruscheweyh differential operator

D^{r}

. We obtain a Fekete–Szegö inequality for certain normalized analytic function defined on the open unit disk for which [...] Read more.

In our present investigation, we introduce and study some new subclasses of analytic functions associated with Ruscheweyh differential operator

D^{r}

. We obtain a Fekete–Szegö inequality for certain normalized analytic function defined on the open unit disk for which

{[{(D^{r} l)}^{'} (z)]}^{ϑ} {(\frac{z {(D^{r} l)}^{'} (z)}{(D^{r} l) (z)})}^{1 - ϑ} ≺ e^{z}

(0 \leq ϑ \leq 1)

lies in a starlike region with respect to 1 and symmetric with respect to the real axis. As a special case of this result, the Fekete–Szegö inequality for a class of functions defined through Poisson distribution series is obtained. Full article

(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)

9 pages, 282 KiB

Open AccessArticle

Applications of the q-Sălăgean Differential Operator Involving Multivalent Functions

by Alina Alb Lupaş

Axioms 2022, 11(10), 512; https://doi.org/10.3390/axioms11100512 - 27 Sep 2022

Cited by 3 | Viewed by 1192

Abstract

In this article we explore several applications of q-calculus in geometric function theory. Using the method of differential subordination, we obtain interesting univalence properties for the q-Sălăgean differential operator. Sharp subordination results are obtained by using functions with remarkable geometric properties as subordinating functions and considering the conditions of expressions involving the q-Sălăgean differential operator and a convex combination using it. Full article

(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)

10 pages, 270 KiB

Open AccessArticle

Applications of Higher-Order q-Derivative to Meromorphic q-Starlike Function Related to Janowski Function

by Likai Liu, Rekha Srivastava and Jin-Lin Liu

Axioms 2022, 11(10), 509; https://doi.org/10.3390/axioms11100509 - 27 Sep 2022

Cited by 2 | Viewed by 959

Abstract

By making use of a higher-order q-derivative operator, certain families of meromorphic q-starlike functions and meromorphic q-convex functions are introduced and studied. Several sufficient conditions and coefficient inequalities for functions in these subclasses are derived. The results presented in this [...] Read more.

(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)

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