The theory of analytic functions is one of the outstanding and elegant subjects of classical mathematics. The study of univalent and multivalent functions is a fascinating aspect of the theory of complex variables, and it is concerned primarily with the interplay of analytic structure and geometric behavior of analytic functions. The rudiments of the theory had already emerged in the beginning of the previous century in the investigations of Koebe in 1907, Gronwall’s proof of the area theorem in 1914, and Bieberbach’s estimates of the second coefficients in 1916. The important aspects concerning the structure and geometric properties in the theory of analytic functions have been studied in more depth during the last few decades. Application and expansion of the theory of univalent and multivalent functions have been employed in numerous fields including differential equations, partial differential equations, fractional calculus, operators theory, and differential subordinations.

This special issue will publish research papers and review articles of the highest quality with appeal to the specialists in a field of complex analysis and to broad mathematical community. We do hope that the distinctive aspects of the issue will bring the reader close to the subject of current research. The most recent developments in the theory will give a thorough and modern approach to the classical theory and present important and compelling applications to the theory of planar harmonic mappings, quasiconformal functions, and dynamical systems.

Potential topics include but are not limited to the following:

• Univalent and multivalent analytic functions
• Planar harmonic mappings
• Special functions and series
• Differential subordination and superordination
• Entire functions
• Conformal and quasi-conformal mappings