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Symmetry
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Symmetry in Geometric Theory of Analytic Functions
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Symmetry in Geometric Theory of Analytic Functions

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 30 April 2024 | Viewed by 12555

Special Issue Editor

Dr. Daciana Alina Alb Lupas

E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, Faculty of Informatics and Sciences, University of Oradea, Universitatii Street, 410087 Oradea, Romania
Interests: topological algebra; geometric function theory; inequalities
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue, titled “Symmetry in Geometric Theory of Analytic Functions”, is addressed to researchers in the complex analysis domain. This Issue will cover all aspects of this topic, starting with special classes of univalent functions, operator-related results, studies using the theory of differential subordination and superordination, or any other techniques which can be applied in the field of complex analysis and its applications, valuing the symmetric properties of the studied object.

The aim of the present Special Issue is to exchange ideas among eminent mathematicians globally as a tribute to the geometric function theory. We hope that this Special Issue will boost cooperation among mathematicians working on a broad variety of pure and applied mathematical areas.

In this Special Issue made up of ideas and mathematical methods, we aim to include a wide area of applications in which the geometric function theory plays an important role, resulting in having an extreme influence on everyday life, as the development of new tools means revolutionary research results have been obtained, bringing scientists even closer to exact science and encouraging the emergence of new approaches, techniques, and perspectives in complex analysis.

Dr. Daciana Alina Alb Lupas
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

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. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • analytic function
  • univalent function
  • harmonic function
  • differential subordination
  • differential superordination
  • strong differential subordination
  • strong differential superordination
  • fuzzy differential subordination
  • fuzzy differential superordination
  • differential operator
  • integral operator
  • differential–integral operator
  • linear operator

Published Papers (15 papers)

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Research

20 pages, 315 KiB  
Article
Differential Subordination and Superordination Using an Integral Operator for Certain Subclasses of p-Valent Functions
by Norah Saud Almutairi, Awatef Shahen and Hanan Darwish
Symmetry 2024, 16(4), 501; https://doi.org/10.3390/sym16040501 - 21 Apr 2024
Viewed by 239
Abstract
This work presents a novel investigation that utilizes the integral operator Ip,λn in the field of geometric function theory, with a specific focus on sandwich theorems. We obtained findings about the differential subordination and superordination of a novel formula [...] Read more.
This work presents a novel investigation that utilizes the integral operator Ip,λn in the field of geometric function theory, with a specific focus on sandwich theorems. We obtained findings about the differential subordination and superordination of a novel formula for a generalized integral operator. Additionally, certain sandwich theorems were discovered. Full article
(This article belongs to the Special Issue Symmetry in Geometric Theory of Analytic Functions)
16 pages, 316 KiB  
Article
On the Analytic Extension of Lauricella–Saran’s Hypergeometric Function FK to Symmetric Domains
by Roman Dmytryshyn and Vitaliy Goran
Symmetry 2024, 16(2), 220; https://doi.org/10.3390/sym16020220 - 11 Feb 2024
Cited by 1 | Viewed by 653
Abstract
In this paper, we consider the representation and extension of the analytic functions of three variables by special families of functions, namely branched continued fractions. In particular, we establish new symmetric domains of the analytical continuation of Lauricella–Saran’s hypergeometric function FK with [...] Read more.
In this paper, we consider the representation and extension of the analytic functions of three variables by special families of functions, namely branched continued fractions. In particular, we establish new symmetric domains of the analytical continuation of Lauricella–Saran’s hypergeometric function FK with certain conditions on real and complex parameters using their branched continued fraction representations. We use a technique that extends the convergence, which is already known for a small domain, to a larger domain to obtain domains of convergence of branched continued fractions and the PC method to prove that they are also domains of analytical continuation. In addition, we discuss some applicable special cases and vital remarks. Full article
(This article belongs to the Special Issue Symmetry in Geometric Theory of Analytic Functions)
13 pages, 316 KiB  
Article
Coefficient Bounds for Two Subclasses of Analytic Functions Involving a Limacon-Shaped Domain
by Daniel Breaz, Trailokya Panigrahi, Sheza M. El-Deeb, Eureka Pattnayak and Srikandan Sivasubramanian
Symmetry 2024, 16(2), 183; https://doi.org/10.3390/sym16020183 - 03 Feb 2024
Viewed by 727
Abstract
In the current exploration, we defined new subclasses of analytic functions, namely Rlim(l,ν) and Clim(l,ν), defined by subordination linked with a Limacon-shaped domain. We found a [...] Read more.
In the current exploration, we defined new subclasses of analytic functions, namely Rlim(l,ν) and Clim(l,ν), defined by subordination linked with a Limacon-shaped domain. We found a few initial coefficient bounds and Fekete–Szegő inequalities for the functions in the above-stated new classes. The corresponding results have been derived for the function h−1. Additionally, we discuss the Poisson distribution as an application of our consequences. Full article
(This article belongs to the Special Issue Symmetry in Geometric Theory of Analytic Functions)
21 pages, 381 KiB  
Article
Geometric Nature of Special Functions on Domain Enclosed by Nephroid and Leminscate Curve
by Reem Alzahrani and Saiful R. Mondal
Symmetry 2024, 16(1), 19; https://doi.org/10.3390/sym16010019 - 22 Dec 2023
Viewed by 1255
Abstract
In this work, the geometric nature of solutions to two second-order differential equations, zy′′(z)+a(z)y′(z)+b(z)y(z)=0 and [...] Read more.
In this work, the geometric nature of solutions to two second-order differential equations, zy′′(z)+a(z)y′(z)+b(z)y(z)=0 and z2y′′(z)+a(z)y′(z)+b(z)y(z)=d(z), is studied. Here, a(z), b(z), and d(z) are analytic functions defined on the unit disc. Using differential subordination, we established that the normalized solution F(z) (with F(0) = 1) of above differential equations maps the unit disc to the domain bounded by the leminscate curve 1+z. We construct several examples by the judicious choice of a(z), b(z), and d(z). The examples include Bessel functions, Struve functions, the Bessel–Sturve kernel, confluent hypergeometric functions, and many other special functions. We also established a connection with the nephroid domain. Directly using subordination, we construct functions that are subordinated by a nephroid function. Two open problems are also suggested in the conclusion. Full article
(This article belongs to the Special Issue Symmetry in Geometric Theory of Analytic Functions)
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12 pages, 1815 KiB  
Article
Certain Results on Subclasses of Analytic and Bi-Univalent Functions Associated with Coefficient Estimates and Quasi-Subordination
by Elaf Ibrahim Badiwi, Waggas Galib Atshan, Ameera N. Alkiffai and Alina Alb Lupas
Symmetry 2023, 15(12), 2208; https://doi.org/10.3390/sym15122208 - 17 Dec 2023
Viewed by 851
Abstract
The purpose of the present paper is to introduce and investigate new subclasses of analytic function class of bi-univalent functions defined in open unit disks connected with a linear q-convolution operator, which are associated with quasi-subordination. We find coefficient estimates of [...] Read more.
The purpose of the present paper is to introduce and investigate new subclasses of analytic function class of bi-univalent functions defined in open unit disks connected with a linear q-convolution operator, which are associated with quasi-subordination. We find coefficient estimates of h2, h3 for functions in these subclasses. Several known and new consequences of these results are also pointed out. There is symmetry between the results of the subclass fq,∑ μ(ζ,n,ρ,σ,ϑ,γ,δ,φ) and the results of the subclass ℵ∑q,δλ,ζ,n,ρ,σ,ϑ,φ. Full article
(This article belongs to the Special Issue Symmetry in Geometric Theory of Analytic Functions)
16 pages, 333 KiB  
Article
Binomial Series-Confluent Hypergeometric Distribution and Its Applications on Subclasses of Multivalent Functions
by Ibtisam Aldawish, Sheza M. El-Deeb and Gangadharan Murugusundaramoorthy
Symmetry 2023, 15(12), 2186; https://doi.org/10.3390/sym15122186 - 11 Dec 2023
Viewed by 726
Abstract
Over the past ten years, analytical functions’ reputation in the literature and their application have grown. We study some practical issues pertaining to multivalent functions with bounded boundary rotation that associate with the combination of confluent hypergeometric functions and binomial series in this [...] Read more.
Over the past ten years, analytical functions’ reputation in the literature and their application have grown. We study some practical issues pertaining to multivalent functions with bounded boundary rotation that associate with the combination of confluent hypergeometric functions and binomial series in this research. A novel subset of multivalent functions is established through the use of convolution products and specific inclusion properties are examined through the application of second order differential inequalities in the complex plane. Furthermore, for multivalent functions, we examined inclusion findings using Bernardi integral operators. Moreover, we will demonstrate how the class proposed in this study, in conjunction with the acquired results, generalizes other well-known (or recently discovered) works that are called out as exceptions in the literature. Full article
(This article belongs to the Special Issue Symmetry in Geometric Theory of Analytic Functions)
14 pages, 310 KiB  
Article
An Application of Touchard Polynomials on Subclasses of Analytic Functions
by Ekram E. Ali, Waffa Y. Kota, Rabha M. El-Ashwah, Abeer M. Albalahi, Fatma E. Mansour and R. A. Tahira
Symmetry 2023, 15(12), 2125; https://doi.org/10.3390/sym15122125 - 29 Nov 2023
Viewed by 753
Abstract
The aim of this work is to discuss some conditions for Touchard polynomials to be in the classes TBb(ρ,σ) and TKb(ρ,σ). Also, we obtain some connection between  [...] Read more.
The aim of this work is to discuss some conditions for Touchard polynomials to be in the classes TBb(ρ,σ) and TKb(ρ,σ). Also, we obtain some connection between Rη(D,E) and TKb(ρ,σ). Also, we investigate several mapping properties involving these subclasses. Further, we discuss the geometric properties of an integral operator related to the Touchard polynomial. Additionally, briefly mentioned are specific instances of our primary results. Also, several particular examples are presented. Full article
(This article belongs to the Special Issue Symmetry in Geometric Theory of Analytic Functions)
25 pages, 1038 KiB  
Article
New Versions of Fuzzy-Valued Integral Inclusion over p-Convex Fuzzy Number-Valued Mappings and Related Fuzzy Aumman’s Integral Inequalities
by Nasser Aedh Alreshidi, Muhammad Bilal Khan, Daniel Breaz and Luminita-Ioana Cotirla
Symmetry 2023, 15(12), 2123; https://doi.org/10.3390/sym15122123 - 28 Nov 2023
Viewed by 643
Abstract
It is well known that both concepts of symmetry and convexity are directly connected. Similarly, in fuzzy theory, both ideas behave alike. It is important to note that real and interval-valued mappings are exceptional cases of fuzzy number-valued mappings ( [...] Read more.
It is well known that both concepts of symmetry and convexity are directly connected. Similarly, in fuzzy theory, both ideas behave alike. It is important to note that real and interval-valued mappings are exceptional cases of fuzzy number-valued mappings (FNVMs) because fuzzy theory depends upon the unit interval that make a significant contribution to overcoming the issues that arise in the theory of interval analysis and fuzzy number theory. In this paper, the new class of p-convexity over up and down (UD) fuzzy relation has been introduced which is known as UD-p-convex fuzzy number-valued mappings (UD-p-convex FNVMs). We offer a thorough analysis of Hermite–Hadamard-type inequalities for FNVMs that are UD-p-convex using the fuzzy Aumann integral. Some previous results from the literature are expanded upon and broadly applied in our study. Additionally, we offer precise justifications for the key theorems that Kunt and İşcan first deduced in their article titled “Hermite–Hadamard–Fejer type inequalities for p-convex functions”. Some new and classical exceptional cases are also discussed. Finally, we illustrate our findings with well-defined examples. Full article
(This article belongs to the Special Issue Symmetry in Geometric Theory of Analytic Functions)
15 pages, 329 KiB  
Article
Analytic Invariants of Semidirect Products of Symmetric Groups on Banach Spaces
by Nataliia Baziv and Andriy Zagorodnyuk
Symmetry 2023, 15(12), 2117; https://doi.org/10.3390/sym15122117 - 27 Nov 2023
Cited by 1 | Viewed by 605
Abstract
We consider algebras of polynomials and analytic functions that are invariant with respect to semidirect products of groups of bounded operators on Banach spaces with symmetric bases. In particular, we consider algebras of so-called block-symmetric and double-symmetric analytic functions on Banach spaces [...] Read more.
We consider algebras of polynomials and analytic functions that are invariant with respect to semidirect products of groups of bounded operators on Banach spaces with symmetric bases. In particular, we consider algebras of so-called block-symmetric and double-symmetric analytic functions on Banach spaces ℓp(Cn) and the homomorphisms of these algebras. In addition, we describe an algebraic basis in the algebra of double-symmetric polynomials and discuss a structure of the spectrum of the algebra of double-symmetric analytic functions on ℓp(Cn). Full article
(This article belongs to the Special Issue Symmetry in Geometric Theory of Analytic Functions)
16 pages, 323 KiB  
Article
New Subclass of Close-to-Convex Functions Defined by Quantum Difference Operator and Related to Generalized Janowski Function
by Suha B. Al-Shaikh, Mohammad Faisal Khan, Mustafa Kamal and Naeem Ahmad
Symmetry 2023, 15(11), 1974; https://doi.org/10.3390/sym15111974 - 25 Oct 2023
Cited by 1 | Viewed by 674
Abstract
This work begins with a discussion of the quantum calculus operator theory and proceeds to develop and investigate a new family of close-to-convex functions in an open unit disk. Considering the quantum difference operator, we define and study a new subclass of close-to-convex [...] Read more.
This work begins with a discussion of the quantum calculus operator theory and proceeds to develop and investigate a new family of close-to-convex functions in an open unit disk. Considering the quantum difference operator, we define and study a new subclass of close-to-convex functions connected with generalized Janowski functions. We prove the necessary and sufficient conditions for functions that belong to newly defined classes, including the inclusion relations and estimations of the coefficients. The Fekete–Szegő problem for a more general class is also discussed. The results of this investigation expand upon those of the previous study. Full article
(This article belongs to the Special Issue Symmetry in Geometric Theory of Analytic Functions)
26 pages, 378 KiB  
Article
Exploring a Special Class of Bi-Univalent Functions: q-Bernoulli Polynomial, q-Convolution, and q-Exponential Perspective
by Timilehin Gideon Shaba, Serkan Araci, Babatunde Olufemi Adebesin and Ayhan Esi
Symmetry 2023, 15(10), 1928; https://doi.org/10.3390/sym15101928 - 17 Oct 2023
Viewed by 917
Abstract
This research article introduces a novel operator termed q-convolution, strategically integrated with foundational principles of q-calculus. Leveraging this innovative operator alongside q-Bernoulli polynomials, a distinctive class of functions emerges, characterized by both analyticity and bi-univalence. The determination of initial coefficients [...] Read more.
This research article introduces a novel operator termed q-convolution, strategically integrated with foundational principles of q-calculus. Leveraging this innovative operator alongside q-Bernoulli polynomials, a distinctive class of functions emerges, characterized by both analyticity and bi-univalence. The determination of initial coefficients within the Taylor-Maclaurin series for this function class is accomplished, showcasing precise bounds. Additionally, explicit computation of the second Hankel determinant is provided. These pivotal findings, accompanied by their corollaries and implications, not only enrich but also extend previously published results. Full article
(This article belongs to the Special Issue Symmetry in Geometric Theory of Analytic Functions)
14 pages, 301 KiB  
Article
The Backward Shift and Two Infinite-Dimension Phenomena in Banach Spaces
by Zoriana Novosad and Andriy Zagorodnyuk
Symmetry 2023, 15(10), 1855; https://doi.org/10.3390/sym15101855 - 02 Oct 2023
Viewed by 683
Abstract
We consider the backward shift operator on a sequence Banach space in the context of two infinite-dimensional phenomena: the existence of topologically transitive operators, and the existence of entire analytic functions of the unbounded type. It is well known that the weighted backward [...] Read more.
We consider the backward shift operator on a sequence Banach space in the context of two infinite-dimensional phenomena: the existence of topologically transitive operators, and the existence of entire analytic functions of the unbounded type. It is well known that the weighted backward shift (for an appropriated weight) is topologically transitive on 1≤p<∞ and on c0. We construct some generalizations of the weighted backward shift for non-separable Banach spaces, which remains topologically transitive. Also, we show that the backward shift, in some sense, generates analytic functions of the unbounded type. We introduce the notion of a generator of analytic functions of the unbounded type on a Banach space and investigate its properties. In addition, we show that, using this operator, one can obtain a quasi-extension operator of analytic functions in a germ of zero for entire analytic functions. The results are supported by examples. Full article
(This article belongs to the Special Issue Symmetry in Geometric Theory of Analytic Functions)
26 pages, 875 KiB  
Article
Analysis of Coefficient-Related Problems for Starlike Functions with Symmetric Points Connected with a Three-Leaf-Shaped Domain
by Huo Tang, Muhammad Arif, Muhammad Abbas, Ferdous M. O. Tawfiq and Sarfraz Nawaz Malik
Symmetry 2023, 15(10), 1837; https://doi.org/10.3390/sym15101837 - 28 Sep 2023
Cited by 1 | Viewed by 968
Abstract
The basic aspect of the research on coefficient problems for numerous families of univalent functions is to describe the coefficients of functions in a specific family by the coefficients of the Carathéodory functions. Thus, in utilizing the inequalities that are known for the [...] Read more.
The basic aspect of the research on coefficient problems for numerous families of univalent functions is to describe the coefficients of functions in a specific family by the coefficients of the Carathéodory functions. Thus, in utilizing the inequalities that are known for the class of Carathéodory functions, coefficient functionals may be examined. Several coefficient problems will be addressed in this study by utilizing the methodology for the abovementioned functions’ family. The family of starlike functions with respect to symmetric points connected to a three-leaf-shaped image domain is the topic of our investigation. Full article
(This article belongs to the Special Issue Symmetry in Geometric Theory of Analytic Functions)
9 pages, 267 KiB  
Article
Coefficient Inequalities and Fekete–Szegö-Type Problems for Family of Bi-Univalent Functions
by Tariq Al-Hawary, Ala Amourah, Hasan Almutairi and Basem Frasin
Symmetry 2023, 15(9), 1747; https://doi.org/10.3390/sym15091747 - 12 Sep 2023
Cited by 1 | Viewed by 564
Abstract
In this study, we present a novel family of holomorphic and bi-univalent functions, denoted as EΩ(η,ε;Ϝ). We establish the coefficient bounds for this family by utilizing the generalized telephone numbers. Additionally, we solve the Fekete–Szegö [...] Read more.
In this study, we present a novel family of holomorphic and bi-univalent functions, denoted as EΩ(η,ε;Ϝ). We establish the coefficient bounds for this family by utilizing the generalized telephone numbers. Additionally, we solve the Fekete–Szegö functional for functions that belong to this family within the open unit disk. Moreover, our results have several consequences. Full article
(This article belongs to the Special Issue Symmetry in Geometric Theory of Analytic Functions)
13 pages, 287 KiB  
Article
On Hankel and Inverse Hankel Determinants of Order Two for Some Subclasses of Analytic Functions
by Nehad Ali Shah, Naseer Bin Turki, Sang-Ro Lee, Seonhui Kang and Jae Dong Chung
Symmetry 2023, 15(9), 1674; https://doi.org/10.3390/sym15091674 - 30 Aug 2023
Viewed by 581
Abstract
In view of the subclass SL*(β), which for β=0 reduces to the class SL*, two more subclasses CL(β) and GL(β) are introduced. For all [...] Read more.
In view of the subclass SL*(β), which for β=0 reduces to the class SL*, two more subclasses CL(β) and GL(β) are introduced. For all these three subclasses, we investigate upper bounds of second Hankel and second inverse Hankel determinates. In most of the cases, the results are sharp. Full article
(This article belongs to the Special Issue Symmetry in Geometric Theory of Analytic Functions)
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