Manuscript Topics

Geometric Function Theory focuses on the geometric properties of analytic functions,particularly the study of univalent functions, their subclasses, and associated coefficient problems. In recent years, special functions and their q-analogues have emerged as powerful tools in this field, providing new approaches to classical problems and enabling researchers to define and investigate different new subclasses of analytic, univalent and bi-univalent functions with a number of geometric properties.

The application of special functions, including for example, Mittag-Leffler functions, Hypergeometric functions, Bessel functions, and their q-analogues, has proven particularly effective in studying coefficient bounds, Fekete-Szegő inequalities, Hankel determinants, and subordination theory. Similarly, discrete distributions such as Poisson, Pascal, and their qanalogues have been successfully employed to construct interesting operators and define new families of analytic and bi-univalent functions.

The role of q-calculus and basic (or q-) polynomials in geometric function theory has gained significant attention due to their natural connections with quantum mechanics, combinatorics and related areas. Research in this direction includes the study of q-starlike and q-convex functions, q-differential operators, and coefficient problems involving q-series expansions.

This Special Issue invites high quality original research articles, comprehensive reviews, and expository papers that explore the connection between special functions,q-calculus,and geometric function theory. We welcome submissions that develop new techniques, establish sharp bounds, introduce novel function classes, or provide innovative applications of special functions to classical problems in geometric function theory.

Key Topics:

Potential topics include but are not limited to the following:  
Coefficient bounds for analytic,univalent, and bi-univalent functions  
Fekete-Szegő inequalities and their generalizations  
Initial coefficient estimates and logarithmic coefficients  
Hankel and Toeplitz determinants for function classes  
Starlike, convex, and close-to-convex functions  
q-starlike and q-convex functions  
Subordination and superordination theory  
Functions related to conic domains, lemniscates, and geometric regions  
Differential and integral operators (including q-analogues)  
Convolution operators and linear operators  
Mittag-Leffler and q-Mittag-Leffler functions  
Hypergeometric and q-Hypergeometric functions  
Bessel and q-Bessel functions  
Orthogonal polynomials (Gegenbauer, Chebyshev, Legendre, Jacobi)  
Error functions and confluent hypergeometric functions  
Discrete distributions (Poisson, Pascal, Binomial) and their q-analogues  
Radius problems and sharp bounds

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