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Symmetry
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Symmetry and Its Applications in Complex Analysis by the Means...
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Symmetry and Its Applications in Complex Analysis by the Means of Special Functions

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

Deadline for manuscript submissions: 31 July 2025 | Viewed by 2134

Special Issue Editor

Dr. Jamal Salah

E-Mail Website
Guest Editor
College of Applied and Health Sciences, A’Sharqiyah University, P.O. Box 42, Ibra 400, Oman
Interests: fractional calculus; complex analysis

Special Issue Information

Dear Colleagues,

For almost a century, complex analysts have been actively engaged in the study of the geometric and mapping features of analytic and harmonic functions. The famous Bieberbach conjecture on the size of the moduli of the Taylor coefficients of univalent analytic functions (1916) and univalent harmonic mappings (1984) was attempted to be resolved by defining and studying a number of subclasses of analytic and harmonic functions with a particular geometric characterization. Geometric function theory has extensively explored functions with rotational and finite-fold symmetry with regard to symmetric (conjugate) locations. Furthermore, the functions or their corresponding expressions that map the unit disk onto domains with a specific symmetry (i.e., with respect to a real or imaginary axis) or that display a particular geometrical shape have been useful in the study of a number of function properties, including distortion, growth and covering theorems, radius problems, inclusion relations, differential inequalities/subordinations, and coefficient bounds/inequalities. Furthermore, by incorporating special functions like fractional calculus operators, q-calculus operators, Mittag–Leffler functions, Lambert series, and numerous other functions with coefficients involving Fibonacci numbers, Touchard polynomials, etc., the study of geometric function theory has been expanded. This Special Issue's objective is to examine and solicit original research articles that highlight the most recent advancements in this field of study and how they apply to other relevant subjects.

Through this Special Issue, scholars from various branches of analysis, geometry, and applied mathematics will be able to collaborate and share ideas on how to use the concept of symmetry to study the characteristics of analytic and harmonic functions. The potential topics include but are not limited to the following:

  • Univalent, bi-univalent and multivalent functions;
  • Harmonic univalent functions;
  • Quasi-conformal mappings;
  • Entire and meromorphic functions;
  • Differential subordination and superordination;
  • Geometric function theory in several complex variables;
  • Special functions;
  • Differential and integral operators in geometric function theory.

Dr. Jamal Salah
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

  • symmetry
  • univalent functions
  • bi-univalent functions
  • multivalent functions
  • fractional calculus
  • q-calculus
  • special functions

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  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
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Further information on MDPI's Special Issue policies can be found here.

Published Papers (4 papers)

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Research

14 pages, 311 KiB  
Article
New Subclass of Meromorphic Functions Defined via Mittag–Leffler Function on Hilbert Space
by Mohammad El-Ityan, Luminita-Ioana Cotîrlă, Tariq Al-Hawary, Suha Hammad, Daniel Breaz and Rafid Buti
Symmetry 2025, 17(5), 728; https://doi.org/10.3390/sym17050728 - 9 May 2025
Viewed by 175
Abstract
In this paper, a novel class of meromorphic functions associated with the Mittag–Leffler function Eμ,ϑ(z) is introduced using the Hilbert space operator. In the punctured symmetric domain ⋓∗, essential properties of this class are systematically [...] Read more.
In this paper, a novel class of meromorphic functions associated with the Mittag–Leffler function Eμ,ϑ(z) is introduced using the Hilbert space operator. In the punctured symmetric domain ⋓∗, essential properties of this class are systematically investigated. These properties include coefficient inequalities, growth and distortion bounds, as well as weighted and arithmetic mean estimates. Furthermore, the extreme points and radii of geometric properties such as close-to-convexity, starlikeness, and convexity are analyzed in detail. Additionally, the Hadamard product (or convolution) is explored to demonstrate the algebraic structure and stability of the introduced function class under this operation. Integral mean inequalities are also established to provide further insights into the behavior of these functions within the given domain. Full article
(This article belongs to the Special Issue Symmetry and Its Applications in Complex Analysis by the Means of Special Functions)
17 pages, 269 KiB  
Article
Loss of Exponential Stability for a Delayed Timoshenko System Symmetrically in Both Viscoelasticity and Fractional Boundary Controls
by Mokhtaria Bouariba Sadoun, Amine Benaissa Cherif, Rachid Bentifour, Keltoum Bouhali, Mohamed Biomy and Khaled Zennir
Symmetry 2025, 17(3), 423; https://doi.org/10.3390/sym17030423 - 12 Mar 2025
Viewed by 383
Abstract
The stability analysis of Timoshenko beam systems that incorporate delays and fractional boundary controls is a complex area of study in the field of viscoelasticity. Our study aims to balance the symmetric influence of internal viscoelastic damping and boundary fractional damping in a [...] Read more.
The stability analysis of Timoshenko beam systems that incorporate delays and fractional boundary controls is a complex area of study in the field of viscoelasticity. Our study aims to balance the symmetric influence of internal viscoelastic damping and boundary fractional damping in a structured way. The goal is to establish a system where both effects contribute symmetrically to the overall stability and dynamics. In this paper, we study the stability of certain hyperbolic evolution problems, in particular, a Timoshenko system in viscoelasticity with fractional time delay and fractional boundary controls. We prove, under assumptions on the data, the lack of exponential stability decay rate when η≥0 and polynomial stability decay rate when η>0 using energy methods. Full article
(This article belongs to the Special Issue Symmetry and Its Applications in Complex Analysis by the Means of Special Functions)
23 pages, 375 KiB  
Article
Sharp Bounds of Hermitian Toeplitz Determinants for Bounded Turning Functions
by Wahid Ullah, Rabia Fayyaz, Daniel Breaz and Luminiţa-Ioana Cotîrlă
Symmetry 2025, 17(3), 407; https://doi.org/10.3390/sym17030407 - 8 Mar 2025
Viewed by 588
Abstract
Hermitian Toeplitz determinants are used in multiple disciplines, including functional analysis, applied mathematics, physics, and engineering sciences. We calculate the sharp upper and lower bounds on the fourth-order Hermitian Toeplitz determinant for the subclass of bounded turning functions associated with the nephroid function [...] Read more.
Hermitian Toeplitz determinants are used in multiple disciplines, including functional analysis, applied mathematics, physics, and engineering sciences. We calculate the sharp upper and lower bounds on the fourth-order Hermitian Toeplitz determinant for the subclass of bounded turning functions associated with the nephroid function represented by Rn. A nephroid function is associated with the geometric shape of a nephroid (a kidney-shaped curve) and refers to a specific type of epicycloid with two cusps. In geometric function theory, a bounded turning function is an analytic function whose derivative has a positive real part, ensuring that its tangent vector does not turn too sharply at any point. Full article
(This article belongs to the Special Issue Symmetry and Its Applications in Complex Analysis by the Means of Special Functions)
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11 pages, 257 KiB  
Article
Comprehensive Subfamilies of Bi-Univalent Functions Defined by Error Function Subordinate to Euler Polynomials
by Tariq Al-Hawary, Basem Frasin and Jamal Salah
Symmetry 2025, 17(2), 256; https://doi.org/10.3390/sym17020256 - 8 Feb 2025
Viewed by 490
Abstract
Recently, several researchers have estimated the Maclaurin coefficients, namely q2 and q3, and the Fekete–Szegö functional problem of functions belonging to some special subfamilies of analytic functions related to certain polynomials, such as Lucas polynomials, Legendrae polynomials, Chebyshev polynomials, and [...] Read more.
Recently, several researchers have estimated the Maclaurin coefficients, namely q2 and q3, and the Fekete–Szegö functional problem of functions belonging to some special subfamilies of analytic functions related to certain polynomials, such as Lucas polynomials, Legendrae polynomials, Chebyshev polynomials, and others. This study obtains the bounds of coefficients q2 and q3, and the Fekete–Szegö functional problem for functions belonging to the comprehensive subfamilies T(ζ,ϵ,δ) and J(φ,δ) of analytic functions in a symmetric domain U, using the imaginary error function subordinate to Euler polynomials. After specializing the parameters used in our main results, a number of new special cases are also obtained. Full article
(This article belongs to the Special Issue Symmetry and Its Applications in Complex Analysis by the Means of Special Functions)
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