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Symmetry
Special Issues
Symmetry Application in Geometric Function Theory
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Symmetry Application in Geometric Function Theory

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

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 3876

Special Issue Editors

Prof. Dr. Saminathan Ponnusamy

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Guest Editor
Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India
Interests: geometric function theory
Prof. Dr. Swadesh Kumar Sahoo

E-Mail Website
Guest Editor
Department of Mathematics, Indian Institute of Technology Indore, Indore 453552, India
Interests: geometric function theory
Dr. Yaxiang Li

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Hunan First Normal University, Changsha 410205, China
Interests: geometric function theory

Special Issue Information

Dear Colleagues,

Geometric function theory is an active research field of mathematics dealing with one and higher-dimensional complex analysis—in particular, with numerous applications in both mathematical sciences and engineering fields (for instance, the theory of harmonic mappings, analysis of PDEs, quasiconformal and quasiregular mappings, special functions, and fluid flow problems). Geometric function theory and symmetry are closely related; for instance, Möbius transformation theory and hyperbolic geometry both use symmetric principles. Additionally, function theory has extensively explored starlike functions with regard to symmetric points. The geometry of mappings and domains can be referred to as geometric function theory.

The main goal of publishing this Special Issue is to promote global cooperation, particularly in symmetry applications in the field of geometric function theory. A wide spectrum of function theorists and geometers from around the world are invited to contribute in order to accomplish this goal. The majority of the Special Issue will focus on the following areas of geometric function theory that are still relevant today: univalent harmonic mappings, hyperbolic-type geometries, function spaces, quasiconformal and quasiregular mappings, and function theory, all of which play a key role in obtaining applications.

The study of geometric analysis, function spaces, and metric measure spaces has attracted an increasing amount of attention in recent years. In physics, mechanics, and other application domains, harmonic mappings and analysis on PDEs have been developed, and they serve as a breakthrough in identifying new issues. Studying the general characteristics of geometric function theory is, thus, very important for science. One of the most significant applications of geometric function theory is found in neuroscience, among other fields of study, through conformal brain mappings.

The purpose of this Special Issue is to present a number of papers that concentrate on symmetry and its uses in geometric function theory. It also hopes to act as a spark for fresh ideas and new cooperative endeavours devoted to exploring the amazing insights into numerous branches of science and engineering.

Prof. Dr. Saminathan Ponnusamy
Prof. Dr. Swadesh Kumar Sahoo
Dr. Yaxiang Li
Guest Editors

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

  • symmetry
  • Möbius and hyperbolic groups
  • univalent functions
  • harmonic and quasiconformal mappings
  • functions spaces
  • hyperbolic-type metric geometry
  • geometric analysis and PDEs

Published Papers (3 papers)

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Research

10 pages, 2234 KiB  
Article
Dynamics of Iterations of the Newton Map of sin(z)
by Aimée Cloutier, Jerry Dwyer, Roger W. Barnard, William D. Stone and G. Brock Williams
Symmetry 2024, 16(2), 162; https://doi.org/10.3390/sym16020162 - 30 Jan 2024
Viewed by 620
Abstract
The dynamical systems of trigonometric functions are explored, with a focus on sz=sin(z) and the fractal image created by iterating the Newton map, Fs(z), of s(z). The basins [...] Read more.
The dynamical systems of trigonometric functions are explored, with a focus on sz=sin(z) and the fractal image created by iterating the Newton map, Fs(z), of s(z). The basins of attraction created from iterating Fs(z) are analyzed, and some bounds are determined for the primary basins of attraction. We further prove x and y-axis symmetry of the Newton map as well as some interesting results on periodic points on the real axis. Full article
(This article belongs to the Special Issue Symmetry Application in Geometric Function Theory)
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16 pages, 341 KiB  
Article
On a Class of Analytic Functions Related to Robertson’s Formula Involving Crescent Shaped Domain and Lemniscate of Bernoulli
by Lech Gruszecki, Adam Lecko, Gangadharan Murugusundaramoorthy and Srikandan Sivasubramanian
Symmetry 2023, 15(4), 875; https://doi.org/10.3390/sym15040875 - 6 Apr 2023
Cited by 1 | Viewed by 1164
Abstract
In this paper, we introduce and study the class of analytic functions in the unit disc, which are derived from Robertson’s analytic formula for starlike functions with respect to a boundary point combined with a subordination involving lemniscate of Bernoulli and crescent shaped [...] Read more.
In this paper, we introduce and study the class of analytic functions in the unit disc, which are derived from Robertson’s analytic formula for starlike functions with respect to a boundary point combined with a subordination involving lemniscate of Bernoulli and crescent shaped domains. Using their symmetry property, the basic geometrical and analytical properties of the introduced classes were proved. Early coefficients and the Fekete–Szegö functional were estimated. Results for both classes were also obtained by applying the theory of differential subordinations. Full article
(This article belongs to the Special Issue Symmetry Application in Geometric Function Theory)
11 pages, 276 KiB  
Article
A New Best Proximity Point Results in Partial Metric Spaces Endowed with a Graph
by Ahmad Aloqaily, Nizar Souayah, Kenan Matawie, Nabil Mlaiki and Wasfi Shatanawi
Symmetry 2023, 15(3), 611; https://doi.org/10.3390/sym15030611 - 28 Feb 2023
Cited by 2 | Viewed by 1378
Abstract
For a given mapping f in the framework of different spaces, the fixed-point equations of the form fx=x can model several problems in different areas, such as differential equations, optimization, and computer science. In this work, the aim is to [...] Read more.
For a given mapping f in the framework of different spaces, the fixed-point equations of the form fx=x can model several problems in different areas, such as differential equations, optimization, and computer science. In this work, the aim is to find the best proximity point and to prove its uniqueness on partial metric spaces where the symmetry condition is preserved for several types of contractive non-self mapping endowed with a graph. Our theorems generalize different results in the literature. In addition, we will illustrate the usability of our outcomes with some examples. The proposed model can be considered as a theoretical foundation for applications to real cases. Full article
(This article belongs to the Special Issue Symmetry Application in Geometric Function Theory)
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