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Symmetry
Special Issues
Geometric Function Theory and Special Functions
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Geometric Function Theory and Special Functions

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

Deadline for manuscript submissions: closed (30 November 2022) | Viewed by 8492

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

Published Papers (6 papers)

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Research

9 pages, 269 KiB  
Article
Some Properties of Janowski Symmetrical Functions
by Fuad Alsarari, Aljazi Alkhammash and Erhan Deniz
Symmetry 2022, 14(12), 2526; https://doi.org/10.3390/sym14122526 - 30 Nov 2022
Viewed by 990
Abstract
In our present work, the concepts of symmetrical functions and the concept of spirallike Janowski functions are combined to define a new class of analytic functions. We give a structural formula for functions in [...] Read more.
In our present work, the concepts of symmetrical functions and the concept of spirallike Janowski functions are combined to define a new class of analytic functions. We give a structural formula for functions in Sη,μ(F,H,λ), a representation theorem, the radius of starlikeness estimates, covering and distortion theorems and integral mean inequalities are obtained. Full article
(This article belongs to the Special Issue Geometric Function Theory and Special Functions)
19 pages, 334 KiB  
Article
Applications of a q-Differential Operator to a Class of Harmonic Mappings Defined by q-Mittag–Leffler Functions
by Mohammad Faisal Khan, Isra Al-shbeil, Shahid Khan, Nazar Khan, Wasim Ul Haq and Jianhua Gong
Symmetry 2022, 14(9), 1905; https://doi.org/10.3390/sym14091905 - 12 Sep 2022
Cited by 3 | Viewed by 1123
Abstract
Many diverse subclasses of analytic functions, q-starlike functions, and symmetric q-starlike functions have been studied and analyzed by using q-analogous values of integral and derivative operators. In this paper, we define a q-analogous value of differential operators for harmonic [...] Read more.
Many diverse subclasses of analytic functions, q-starlike functions, and symmetric q-starlike functions have been studied and analyzed by using q-analogous values of integral and derivative operators. In this paper, we define a q-analogous value of differential operators for harmonic functions with the help of basic concepts of quantum (q-) calculus operator theory; and introduce a new subclass of harmonic functions associated with the Janowski and q-Mittag–Leffler functions. We obtain several useful properties of the new class, such as necessary and sufficient conditions, criteria for analyticity, compactness, convexity, extreme points, radii of starlikeness, radii of convexity, distortion bounds, and integral mean inequality. Furthermore, we discuss some applications of this study in the form of some results and examples and highlight some known corollaries for verifying our main results presented in this investigation. Finally, the conclusion section summarizes the fact about the (p,q)-variations. Full article
(This article belongs to the Special Issue Geometric Function Theory and Special Functions)
14 pages, 305 KiB  
Article
Results on Univalent Functions Defined by q-Analogues of Salagean and Ruscheweh Operators
by Ebrahim Amini, Mojtaba Fardi, Shrideh Al-Omari and Kamsing Nonlaopon
Symmetry 2022, 14(8), 1725; https://doi.org/10.3390/sym14081725 - 18 Aug 2022
Cited by 8 | Viewed by 1241
Abstract
In this paper, we define and discuss properties of various classes of analytic univalent functions by using modified q-Sigmoid functions. We make use of an idea of Salagean to introduce the q-analogue of the Salagean differential operator. In addition, we derive [...] Read more.
In this paper, we define and discuss properties of various classes of analytic univalent functions by using modified q-Sigmoid functions. We make use of an idea of Salagean to introduce the q-analogue of the Salagean differential operator. In addition, we derive families of analytic univalent functions associated with new q-Salagean and q-Ruscheweh differential operators. In addition, we obtain coefficient bounds for the functions in such new subclasses of analytic functions and establish certain growth and distortion theorems. By using the concept of the (q, δ)-neighbourhood, we provide several inclusion symmetric relations for certain (q, δ)-neighbourhoods of analytic univalent functions of negative coefficients. Various q-inequalities are also discussed in more details. Full article
(This article belongs to the Special Issue Geometric Function Theory and Special Functions)
11 pages, 304 KiB  
Article
Convolution Properties of q-Janowski-Type Functions Associated with (x,y)-Symmetrical Functions
by Fuad Alsarari and Samirah Alzahrani
Symmetry 2022, 14(7), 1406; https://doi.org/10.3390/sym14071406 - 8 Jul 2022
Cited by 4 | Viewed by 963
Abstract
The purpose of this paper is to define new classes of analytic functions by amalgamating the concepts of q-calculus, Janowski type functions and (x,y)-symmetrical functions. We use the technique of convolution and quantum calculus to investigate the [...] Read more.
The purpose of this paper is to define new classes of analytic functions by amalgamating the concepts of q-calculus, Janowski type functions and (x,y)-symmetrical functions. We use the technique of convolution and quantum calculus to investigate the convolution conditions which will be used as a supporting result for further investigation in our work, we deduce the sufficient conditions, Po´lya-Schoenberg theorem and the application. Finally motivated by definition of the neighborhood, we give analogous definition of neighborhood for the classes S˜qx,y(α,β) and K˜qx,y(α,β), and then investigate the related neighborhood results, which are also pointed out. Full article
(This article belongs to the Special Issue Geometric Function Theory and Special Functions)
14 pages, 308 KiB  
Article
Hankel Determinants and Coefficient Estimates for Starlike Functions Related to Symmetric Booth Lemniscate
by Mohsan Raza, Amina Riaz, Qin Xin and Sarfraz Nawaz Malik
Symmetry 2022, 14(7), 1366; https://doi.org/10.3390/sym14071366 - 2 Jul 2022
Cited by 11 | Viewed by 1617
Abstract
In this paper, we find Hankel determinants and coefficient bounds for a subclass of starlike functions related to Booth lemniscate. In particular, we obtain the first four sharp coefficient bounds, Hankel determinants of order two and three, and Zalcman conjecture for this class [...] Read more.
In this paper, we find Hankel determinants and coefficient bounds for a subclass of starlike functions related to Booth lemniscate. In particular, we obtain the first four sharp coefficient bounds, Hankel determinants of order two and three, and Zalcman conjecture for this class of functions. Full article
(This article belongs to the Special Issue Geometric Function Theory and Special Functions)
11 pages, 412 KiB  
Article
Application of Einstein Function on Bi-Univalent Functions Defined on the Unit Disc
by Alaa H. El-Qadeem, Mohamed A. Mamon and Ibrahim S. Elshazly
Symmetry 2022, 14(4), 758; https://doi.org/10.3390/sym14040758 - 6 Apr 2022
Cited by 4 | Viewed by 1479
Abstract
Motivated by q-calculus, we define a new family of Σ, which is the family of bi-univalent analytic functions in the open unit disc U that is related to the Einstein function E(z). We establish estimates for the first [...] Read more.
Motivated by q-calculus, we define a new family of Σ, which is the family of bi-univalent analytic functions in the open unit disc U that is related to the Einstein function E(z). We establish estimates for the first two Taylor–Maclaurin coefficients |a2|, |a3|, and the Fekete–Szegö inequality a3−μa22 for the functions that belong to these families. Full article
(This article belongs to the Special Issue Geometric Function Theory and Special Functions)
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