New Trends in Geometric Function Theory

Dear Colleagues,

Geometric function theory began to develop as a separate branch of complex analysis in the early twentieth century when the first major works appeared in this field due to P. Koebe, T.H. Gromwall, I. W. Alexander and L. Bieberbach. In 1916, L. Bieberbach expressed the famous hypothesis that bears his name, which could only have been proved in 1984 by Louis de Branges and has driven research in the field of univalent functions for nearly a century. Additionally, new methods have been developed, such as L. Loewner’s parametric method, the variational method initiated by M. Schiffer and G. M. Goluzin, the method of integral representations introduced by G. Herglotz, the method of extreme points by L. Brickman and T.H. Mac-Gregor, the method of differential subordinations due to S.S. Miller and P.T. Mocanu, and so on. Recently, new study directions have emerged, such as strong differential subordinations and superordinations theory, fuzzy differential subordinations and superordinations theory, and applications of special functions and of quantum calculus in geometric functions theory.

The focus of this Special Issue is to continue to advance research on topics relating to the new trends in geometric functions theory and its applications.  Topics that are invited for submission include (but are not limited to):

• univalent function and multivalent functions
• applications of special functions in geometric functions theory
• differential subordinations and superordinations
• fuzzy differential subordinations and superordinations
• differential and integral operators
• holomorphic mappings and correspondences
• holomorphic functions of several complex variables
• applications quantum calculus in geometric functions theory
• univalence criteria

Prof. Dr. Acu Mugur Alexandru
Dr. Shahram Najafzadeh
Guest Editors

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