Avkhadiev–Backer type p-valent conditions for biharmonic functions

Abstract

This paper is devoted to locally univalent complex-valued biharmonic functions. We obtain subclasses of biharmonic multivalet functions and get certain sufficient conditions for functions to be in these classes. We construct new families of biharmonic univalent and p-valent mappings of the unit disk similar to Avkhadiev–Becker type conditions for analytic functions. We also consider biharmonic functions defined in the exterior of the unit disk. New univalent and p-valent conditions for harmonic mappings of the unit disk are obtained.