Research

11 pages, 293 KiB

Open AccessArticle

Applications of Horadam Polynomials for Bazilevič and λ-Pseudo-Starlike Bi-Univalent Functions Associated with Sakaguchi Type Functions

by Isra Al-Shbeil, Abbas Kareem Wanas, Hala AlAqad, Adriana Cătaş and Hanan Alohali

Symmetry 2024, 16(2), 218; https://doi.org/10.3390/sym16020218 - 11 Feb 2024

Viewed by 635

Abstract

In this study, we introduce a new class of normalized analytic and bi-univalent functions denoted by

D_{Σ} (δ, η, λ, t, r)

. These functions are connected to the Bazilevič functions and the

λ

-pseudo-starlike functions. [...] Read more.

In this study, we introduce a new class of normalized analytic and bi-univalent functions denoted by

D_{Σ} (δ, η, λ, t, r)

. These functions are connected to the Bazilevič functions and the

λ

-pseudo-starlike functions. We employ Sakaguchi Type Functions and Horadam polynomials in our survey. We establish the Fekete-Szegö inequality for the functions in

D_{Σ} (δ, η, λ, t, r)

and derive upper bounds for the initial Taylor–Maclaurin coefficients

| a_{2} |

and

| a_{3} |

. Additionally, we establish connections between our results and previous research papers on this topic. Full article

(This article belongs to the Special Issue Selected Papers from International Symposium on Geometric Function Theory and Applications (GFTA))

13 pages, 307 KiB

Open AccessArticle

Sharp Estimates Involving a Generalized Symmetric Sălăgean q-Differential Operator for Harmonic Functions via Quantum Calculus

by Isra Al-Shbeil, Shahid Khan, Fairouz Tchier, Ferdous M. O. Tawfiq, Amani Shatarah and Adriana Cătaş

Symmetry 2023, 15(12), 2156; https://doi.org/10.3390/sym15122156 - 04 Dec 2023

Cited by 1 | Viewed by 598

Abstract

In this study, we apply q-symmetric calculus operator theory and investigate a generalized symmetric Sălăgean q-differential operator for harmonic functions in an open unit disk. We consider a newly defined operator and establish new subclasses of harmonic functions in complex order. [...] Read more.

In this study, we apply q-symmetric calculus operator theory and investigate a generalized symmetric Sălăgean q-differential operator for harmonic functions in an open unit disk. We consider a newly defined operator and establish new subclasses of harmonic functions in complex order. We determine the sharp results, such as the sufficient necessary coefficient bounds, the extreme of closed convex hulls, and the distortion theorems for a new family of harmonic functions. Further, we illustrate how we connect the findings of previous studies and the results of this article. Full article

(This article belongs to the Special Issue Selected Papers from International Symposium on Geometric Function Theory and Applications (GFTA))

12 pages, 309 KiB

Open AccessArticle

Study on the Criteria for Starlikeness in Integral Operators Involving Bessel Functions

by Georgia Irina Oros, Gheorghe Oros and Daniela Andrada Bardac-Vlada

Symmetry 2023, 15(11), 1976; https://doi.org/10.3390/sym15111976 - 26 Oct 2023

Cited by 1 | Viewed by 641

Abstract

The study presented in this paper follows a line of research familiar for Geometric Function Theory, which consists in defining new integral operators and conducting studies for revealing certain geometric properties of those integral operators such as univalence, starlikness, or convexity. The present [...] Read more.

The study presented in this paper follows a line of research familiar for Geometric Function Theory, which consists in defining new integral operators and conducting studies for revealing certain geometric properties of those integral operators such as univalence, starlikness, or convexity. The present research focuses on the Bessel function of the first kind and order

ν

unveiling the conditions for this function to be univalent and further using its univalent form in order to define a new integral operator on the space of holomorphic functions. For particular values of the parameters implicated in the definition of the new integral operator involving the Bessel function of the first kind, the well-known Alexander, Libera, and Bernardi integral operators can be obtained. In the first part of the study, necessary and sufficient conditions are obtained for the Bessel function of the first kind and order

ν

to be a starlike function or starlike of order

α \in [0, 1)

. The renowned prolific method of differential subordination due to Sanford S. Miller and Petru T. Mocanu is employed in the reasoning. In the second part of the study, the outcome of the first part is applied in order to introduce the new integral operator involving the form of the Bessel function of the first kind, which is starlike. Further investigations disclose the necessary and sufficient conditions for this new integral operator to be starlike or starlike of order

\frac{1}{2}

. Full article

(This article belongs to the Special Issue Selected Papers from International Symposium on Geometric Function Theory and Applications (GFTA))

12 pages, 274 KiB

Open AccessArticle

On Classes of Meromorphic Functions Defined by Subordination and Convolution

by Luminiţa-Ioana Cotîrlă and Elisabeta-Alina Totoi

Symmetry 2023, 15(9), 1763; https://doi.org/10.3390/sym15091763 - 15 Sep 2023

Viewed by 517

Abstract

For

p \in N^{*}

, let

Σ_{p}

denote the class of meromorphic p-valent functions. We consider an operator for meromorphic functions denoted by

T_{b}^{n}

, which generalizes some previously studied operators. We introduce some new subclasses of the class [...] Read more.

For

p \in N^{*}

, let

Σ_{p}

denote the class of meromorphic p-valent functions. We consider an operator for meromorphic functions denoted by

T_{b}^{n}

, which generalizes some previously studied operators. We introduce some new subclasses of the class

Σ_{p}

, associated with subordination using the above operator, and we prove that these classes are preserved regarding the operator

J_{p, γ}

, so we have symmetry when we look at the form of the class in which we consider the function g and at the form of the class of the image

J_{p, γ} (g)

, where

J_{p, γ} (g) (z) = \frac{γ - p}{z^{γ}} \int_{0}^{z} g (t) t^{γ - 1} d t

,

γ \in C

with

Re γ > p

. Full article

(This article belongs to the Special Issue Selected Papers from International Symposium on Geometric Function Theory and Applications (GFTA))

19 pages, 324 KiB

Open AccessArticle

New Results on a Fractional Integral of Extended Dziok–Srivastava Operator Regarding Strong Subordinations and Superordinations

by Alina Alb Lupaş

Symmetry 2023, 15(8), 1544; https://doi.org/10.3390/sym15081544 - 05 Aug 2023

Cited by 1 | Viewed by 556

Abstract

In 2012, new classes of analytic functions on

U \times \bar{U}

with coefficient holomorphic functions in

\bar{U}

were defined to give a new approach to the concepts of strong differential subordination and strong differential superordination. Using those new classes, the extended [...] Read more.

In 2012, new classes of analytic functions on

U \times \bar{U}

with coefficient holomorphic functions in

\bar{U}

were defined to give a new approach to the concepts of strong differential subordination and strong differential superordination. Using those new classes, the extended Dziok–Srivastava operator is introduced in this paper and, applying fractional integral to the extended Dziok–Srivastava operator, we obtain a new operator

D_{z}^{- γ} H_{m}^{l} [α_{1}, β_{1}]

that was not previously studied using the new approach on strong differential subordinations and superordinations. In the present article, the fractional integral applied to the extended Dziok–Srivastava operator is investigated by applying means of strong differential subordination and superordination theory using the same new classes of analytic functions on

U \times \bar{U} .

Several strong differential subordinations and superordinations concerning the operator

D_{z}^{- γ} H_{m}^{l} [α_{1}, β_{1}]

are established, and the best dominant and best subordinant are given for each strong differential subordination and strong differential superordination, respectively. This operator may have symmetric or asymmetric properties. Full article

(This article belongs to the Special Issue Selected Papers from International Symposium on Geometric Function Theory and Applications (GFTA))

11 pages, 307 KiB

Open AccessArticle

New Applications of Gaussian Hypergeometric Function for Developments on Third-Order Differential Subordinations

by Georgia Irina Oros, Gheorghe Oros and Lavinia Florina Preluca

Symmetry 2023, 15(7), 1306; https://doi.org/10.3390/sym15071306 - 25 Jun 2023

Cited by 1 | Viewed by 704

Abstract

The main objective of this paper is to present classical second-order differential subordination knowledge extended in this study to include new results regarding third-order differential subordinations. The focus of this study is on the main problems examined by differential subordination theory. Hence, the [...] Read more.

The main objective of this paper is to present classical second-order differential subordination knowledge extended in this study to include new results regarding third-order differential subordinations. The focus of this study is on the main problems examined by differential subordination theory. Hence, the new results obtained here reveal techniques for identifying dominants and the best dominant of certain third-order differential subordinations. Another aspect of novelty is the new application of the Gaussian hypergeometric function. Novel third-order differential subordination results are obtained using the best dominant provided by the theorems and the operator previously defined as Gaussian hypergeometric function’s fractional integral. The research investigation is concluded by giving an example of how the results can be implemented. Full article

(This article belongs to the Special Issue Selected Papers from International Symposium on Geometric Function Theory and Applications (GFTA))

12 pages, 299 KiB

Open AccessArticle

Radius Results for Certain Strongly Starlike Functions

by Afis Saliu, Kanwal Jabeen, Qin Xin, Fairouz Tchier and Sarfraz Nawaz Malik

Symmetry 2023, 15(5), 1124; https://doi.org/10.3390/sym15051124 - 21 May 2023

Viewed by 877

Abstract

This article comprises the study of strongly starlike functions which are defined by using the concept of subordination. The function

φ

defined by

φ (ζ) = {(1 + ζ)}^{λ}

,

0 < λ < 1

maps the open [...] Read more.

This article comprises the study of strongly starlike functions which are defined by using the concept of subordination. The function

φ

defined by

φ (ζ) = {(1 + ζ)}^{λ}

,

0 < λ < 1

maps the open unit disk in the complex plane to a domain symmetric with respect to the real axis in the right-half plane. Using this mapping, we obtain some radius results for a family of starlike functions. It is worth noting that all the presented results are sharp. Full article

(This article belongs to the Special Issue Selected Papers from International Symposium on Geometric Function Theory and Applications (GFTA))

21 pages, 536 KiB

Open AccessArticle

Starlike Functions Associated with Secant Hyperbolic Function

by Khadija Bano, Mohsan Raza, Qin Xin, Fairouz Tchier and Sarfraz Nawaz Malik

Symmetry 2023, 15(3), 737; https://doi.org/10.3390/sym15030737 - 16 Mar 2023

Cited by 3 | Viewed by 1268

Abstract

Motivated by the recent work on the symmetric domains, this article investigates certain features of symmetric domain which are caused by the secant hyperbolic functions. Geometric characteristics of analytic functions associated with secant hyperbolic functions are discussed, which include the inclusion results, structural [...] Read more.

Motivated by the recent work on the symmetric domains, this article investigates certain features of symmetric domain which are caused by the secant hyperbolic functions. Geometric characteristics of analytic functions associated with secant hyperbolic functions are discussed, which include the inclusion results, structural formula, certain sharp radii results such as radius of starlikeness and convexity of order

α .

It also finds a radius for ratios of analytic functions associated with Euler numbers. Full article

(This article belongs to the Special Issue Selected Papers from International Symposium on Geometric Function Theory and Applications (GFTA))

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16 pages, 321 KiB

Open AccessArticle

Strong Differential Subordination and Superordination Results for Extended q-Analogue of Multiplier Transformation

by Alina Alb Lupaş and Firas Ghanim

Symmetry 2023, 15(3), 713; https://doi.org/10.3390/sym15030713 - 13 Mar 2023

Cited by 3 | Viewed by 1030

Abstract

The results obtained by the authors in the present article refer to quantum calculus applications regarding the theories of strong differential subordination and superordination. The q-analogue of the multiplier transformation is extended, in order to be applied on the specific classes of [...] Read more.

The results obtained by the authors in the present article refer to quantum calculus applications regarding the theories of strong differential subordination and superordination. The q-analogue of the multiplier transformation is extended, in order to be applied on the specific classes of functions involved in strong differential subordination and superordination theories. Using this extended q-analogue of the multiplier transformation, a new class of analytic normalized functions is introduced and investigated. The convexity of the set of functions belonging to this class is proven and the symmetry properties derive from this characteristic of the class. Additionally, due to the convexity of the functions contained in this class, interesting strong differential subordination results are proven using the extended q-analogue of the multiplier transformation. Furthermore, strong differential superordination theory is applied to the extended q-analogue of the multiplier transformation for obtaining strong differential superordinations for which the best subordinants are provided. Full article

(This article belongs to the Special Issue Selected Papers from International Symposium on Geometric Function Theory and Applications (GFTA))

8 pages, 294 KiB

Open AccessArticle

Applications of Laguerre Polynomials for Bazilevič and θ-Pseudo-Starlike Bi-Univalent Functions Associated with Sakaguchi-Type Functions

by Luminiţa-Ioana Cotîrlǎ and Abbas Kareem Wanas

Symmetry 2023, 15(2), 406; https://doi.org/10.3390/sym15020406 - 03 Feb 2023

Cited by 4 | Viewed by 927

Abstract

The aim of the present article is to introduce and investigate a new family

L_{Σ} (δ, η, θ, t; h)

of normalized holomorphic and bi-univalent functions that involve the Sakaguchi-type Bazilevič functions and Sakaguchi-type

θ

-pseudo-starlike [...] Read more.

The aim of the present article is to introduce and investigate a new family

L_{Σ} (δ, η, θ, t; h)

of normalized holomorphic and bi-univalent functions that involve the Sakaguchi-type Bazilevič functions and Sakaguchi-type

θ

-pseudo-starlike functions associated with Laguerre polynomials. We obtain estimates on the initial Taylor–Maclaurin coefficients and the Fekete–Szegö problem for functions in this family. Properties of symmetry can be studied for this newly family of functions. Full article

(This article belongs to the Special Issue Selected Papers from International Symposium on Geometric Function Theory and Applications (GFTA))

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