Current Topics in Geometric Function Theory, 2nd Edition

Dear Colleagues,

One of the most studied branches in the theory of functions of one complex variable, concerned with the study of the geometric properties of analytical functions in complex analysis, the geometric theory of analytic functions (also called geometric function theory (GFT)) has the Riemann mapping theorem at its core, formulated by B. Riemann in 1851 and approached later by others, such as C. Carathéodory, P. Koebe, and L. Bieberbach. The duality of this field, based on the tradeoff between an analytical approach and geometric intuition, constitutes an advantage when we want to study the geometrical behavior of various classes of functions. The current development of the geometric function theory involving both classic and modern topics also generates many connections with various fields of mathematics, including special functions, probability distributions, fractional, and q-calculus. Even if the geometric function theory is mostly viewed as a theoretical domain, significant practical applications were also obtained from the theoretical results in different fields, such as fluid mechanics, nuclear physics, mathematical physics, astrophysics, and, more recently, in control theory, signal and image processing, and others.

This Special Issue aims to be a collection of original and recent research in the current topics of the field of geometric function theory related, but not restricted, to univalent function theory; the study of star-like, convex, and other classes of analytic functions with geometric properties; the study of integral operators; differential subordination and superordination; and the newly flourishing research area based on q-calculus and fractional calculus. Research papers focusing on the geometric function theory used in real-life applications are also encouraged for this Special Issue.

We are looking forward to receiving original contributions that can broaden the horizons of this research area. 

Prof. Dr. Nicoleta Breaz
Guest Editor

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