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Symmetry
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Geometric Function Theory and Special Functions II
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Geometric Function Theory and Special Functions II

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

Deadline for manuscript submissions: 14 February 2025 | Viewed by 5533

Special Issue Editor

Prof. Dr. Erhan Deniz

E-Mail Website
Guest Editor
Department of Mathematics, Kafkas University, Kars 36100, Turkey
Interests: complex analysis; analytic functions; univalent functions; special functions
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Geometric Function Theory is the branch of complex analysis that studies the geometric properties of analytic functions. It was born around the turn of the 20th century and remains one of the active fields of the current research. It is very important for us to find new observational and theoretical results in this field with various applications. In particular, geometric properties of special functions such as Bessel, Struve, Lommel, and Mittag–Leffler functions have drawn attention recently. Moreover, functions with rotational symmetry and finite-fold symmetry, with respect to symmetric (conjugate) points, have been widely studied in geometric function theory.

The main aim of the Special Issue is to invite the authors to submit original research articles that not only provide new results or methods but may also have a great impact on other people in their efforts to broaden their knowledge and investigation and will stimulate the efforts in developing new results in Geometric Function Theory and special functions. Review articles with some open problems are also welcome. We do hope that the distinctive aspects of the issue will bring the reader close to the subject of current research and leave the way open for a more direct and less ambivalent approach to the topic.

This Special Issue will contain high-quality papers on current related topics written by world-leading experts in the area.

Prof. Dr. Erhan Deniz
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

  • conformal mapping theory
  • differential subordinations and superordinations
  • entire and meromorphic functions
  • fractional calculus with applications
  • general theory of univalent and multivalent functions
  • harmonic functions
  • quasiconformal mappings
  • special functions and applications

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Published Papers (6 papers)

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Research

13 pages, 782 KiB  
Article
Results on Third-Order Differential Subordination for Analytic Functions Related to a New Integral Operator
by Sara Falih Maktoof, Waggas Galib Atshan and Ameera N. Alkiffai
Symmetry 2024, 16(11), 1453; https://doi.org/10.3390/sym16111453 - 1 Nov 2024
Viewed by 457
Abstract
In this paper, we aim to give some results for third-order differential subordination for analytic functions in the open unit disk U=z:z∈C and z<1 involving the new integral operator [...] Read more.
In this paper, we aim to give some results for third-order differential subordination for analytic functions in the open unit disk U=z:z∈C and z<1 involving the new integral operator μα,nm(f∗g). The results are obtained by examining pertinent classes of acceptable functions. New findings on differential subordination have been obtained. Additionally, some specific cases are documented. This work investigates appropriate classes of admissible functions, presents a novel of new integral operator, and discusses the properties of third-order differential subordination. The properties and results of the differential subordination are symmetrical to the properties of the differential superordination to form the sandwich theorems. Full article
(This article belongs to the Special Issue Geometric Function Theory and Special Functions II)
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16 pages, 331 KiB  
Article
Some Classes of Bazilevič-Type Close-to-Convex Functions Involving a New Derivative Operator
by Pishtiwan Othman Sabir, Alina Alb Lupas, Sipal Saeed Khalil, Pshtiwan Othman Mohammed and Mohamed Abdelwahed
Symmetry 2024, 16(7), 836; https://doi.org/10.3390/sym16070836 - 3 Jul 2024
Cited by 1 | Viewed by 935
Abstract
In the present paper, we are merging two interesting and well-known classes, namely those of Bazilevič and close-to-convex functions associated with a new derivative operator. We derive coefficient estimates for this broad category of analytic, univalent and bi-univalent functions and draw attention to [...] Read more.
In the present paper, we are merging two interesting and well-known classes, namely those of Bazilevič and close-to-convex functions associated with a new derivative operator. We derive coefficient estimates for this broad category of analytic, univalent and bi-univalent functions and draw attention to the Fekete–Szegö inequalities relevant to functions defined within the open unit disk. Additionally, we identify several specific special cases of our results by specializing the parameters. Full article
(This article belongs to the Special Issue Geometric Function Theory and Special Functions II)
16 pages, 305 KiB  
Article
Second Hankel Determinant and Fekete–Szegö Problem for a New Class of Bi-Univalent Functions Involving Euler Polynomials
by Semh Kadhim Gebur and Waggas Galib Atshan
Symmetry 2024, 16(5), 530; https://doi.org/10.3390/sym16050530 - 28 Apr 2024
Viewed by 752
Abstract
Orthogonal polynomials have been widely employed by renowned authors within the context of geometric function theory. This study is driven by prior research and aims to address the —Fekete-Szegö problem. Additionally, we provide bound estimates for the coefficients and an upper bound estimate [...] Read more.
Orthogonal polynomials have been widely employed by renowned authors within the context of geometric function theory. This study is driven by prior research and aims to address the —Fekete-Szegö problem. Additionally, we provide bound estimates for the coefficients and an upper bound estimate for the second Hankel determinant for functions belonging to the category of analytical and bi-univalent functions. This investigation incorporates the utilization of Euler polynomials. Full article
(This article belongs to the Special Issue Geometric Function Theory and Special Functions II)
9 pages, 238 KiB  
Article
A New Subclass of Analytic Functions Associated with the q-Derivative Operator Related to the Pascal Distribution Series
by Ying Yang, Rekha Srivastava and Jin-Lin Liu
Symmetry 2024, 16(3), 280; https://doi.org/10.3390/sym16030280 - 28 Feb 2024
Cited by 1 | Viewed by 1004
Abstract
A new subclass TXq[λ,A,B] of analytic functions is introduced by making use of the q-derivative operator associated with the Pascal distribution. Certain properties of analytic functions in the subclass TXq[λ,A,B] are derived. Some known results are generalized. Full article
(This article belongs to the Special Issue Geometric Function Theory and Special Functions II)
10 pages, 1511 KiB  
Article
On Third Hankel Determinant for Certain Subclass of Bi-Univalent Functions
by Qasim Ali Shakir and Waggas Galib Atshan
Symmetry 2024, 16(2), 239; https://doi.org/10.3390/sym16020239 - 16 Feb 2024
Cited by 4 | Viewed by 948
Abstract
This study presents a subclass S(β) of bi-univalent functions within the open unit disk region D. The objective of this class is to determine the bounds of the Hankel determinant of order 3, (Ⱨ3(1) [...] Read more.
This study presents a subclass S(β) of bi-univalent functions within the open unit disk region D. The objective of this class is to determine the bounds of the Hankel determinant of order 3, (Ⱨ3(1)). In this study, new constraints for the estimates of the third Hankel determinant for the class S(β) are presented, which are of considerable interest in various fields of mathematics, including complex analysis and geometric function theory. Here, we define these bi-univalent functions as S(β) and impose constraints on the coefficients │an│. Our investigation provides the upper bounds for the bi-univalent functions in this newly developed subclass, specifically for n = 2, 3, 4, and 5. We then derive the third Hankel determinant for this particular class, which reveals several intriguing scenarios. These findings contribute to the broader understanding of bi-univalent functions and their potential applications in diverse mathematical contexts. Notably, the results obtained may serve as a foundation for future investigations into the properties and applications of bi-univalent functions and their subclasses. Full article
(This article belongs to the Special Issue Geometric Function Theory and Special Functions II)
12 pages, 274 KiB  
Article
Integral Operators Applied to Classes of Convex and Close-to-Convex Meromorphic p-Valent Functions
by Elisabeta-Alina Totoi and Luminita-Ioana Cotirla
Symmetry 2023, 15(11), 2079; https://doi.org/10.3390/sym15112079 - 17 Nov 2023
Viewed by 771
Abstract
We consider a newly introduced integral operator that depends on an analytic normalized function and generalizes many other previously studied operators. We find the necessary conditions that this operator has to meet in order to preserve convex meromorphic functions. We know that convexity [...] Read more.
We consider a newly introduced integral operator that depends on an analytic normalized function and generalizes many other previously studied operators. We find the necessary conditions that this operator has to meet in order to preserve convex meromorphic functions. We know that convexity has great impact in the industry, linear and non-linear programming problems, and optimization. Some lemmas and remarks helping us to obtain complex functions with positive real parts are also given. Full article
(This article belongs to the Special Issue Geometric Function Theory and Special Functions II)
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