Analytic and geometric properties of some univalent harmonic functions

Abstract

Harmonic univalent functions play a pivotal role in the fields of fluid dynamics, minimal graphs, robotics etc. Generating new harmonic univalent functions and to study their geometric and analytic properties is one of the esteemed topics in the field of Geometric Function Theory. Till now, many techniques have come into existence which help us to construct new univalent harmonic functions, for example, shear construction, taking transformations, taking convolutions and taking convex combinations etc. Our main motive of the present research is to remodel these techniques and establish new results. The present work is organized in the form of seven chapters newline