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 1793

Special Issue Editor


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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

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Keywords

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

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Published Papers (3 papers)

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Research

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 349
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 η0 and polynomial stability decay rate when η>0 using energy methods. Full article
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 544
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
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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 454
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
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