Geometric function theory (GFT) is one of the most important branches of complex analysis. GFT is concerned with the study of the geometric properties of analytical functions in complex analysis and has many applications in various fields of mathematics, including special functions, probability distributions, dynamical systems, fractional calculus, and analytic number theory. In recent years, there has been remarkable progress in the theory of geometric functions and their various applications.

A function f(z) that is analytic in the open unit disk U is said to be univalent in U, if it assumes no value more than once in U. Univalent function theory is a new area of great interest in GFT, which has branched out to include many fields, such as classes of p-valent functions, bi-univalent functions, starlike and convex functions, and other many classes which have geometric properties of analytic functions. GFT has also extended to other branches, including analytic integral operators, and subordination and superordination-preserving operators, among many others.

The aim of this Special Issue is to shed light on the most important developments and new research in the field of geometric function theory and their applications. We invite original papers and review articles in various fields of mathematics related to geometric function theory in complex analysis, and we hope to shed light on contributions to the development of this important branch. This Special Issue will cover all aspects of topics related to geometric function theory and its applications.

Potential topics include but are not limited to the following:

• Analytic Functions in GFT
• Univalent functions associated with GFT
• Multivalent functions associated with GFT
• Conformal maps
• Quasiconformal maps
• Differential subordinations and superordinations
• Fractional calculus and applications in GFT
• Analytic continuation
• Operators in GFT
• Applications in GFT
• Extremal problems in GFT