Analytic and geometric properties of certain univalent functions

Abstract

KEYWORDS: Analytic functions, Approximations of analytic functions, Area problem, Close-to-convex functions, Convex functions, Dirichlet nite, Karush- Kuhn-Tucker conditions, Meromorphic functions, Meromorphically convex functions, Quadratic programming, Quasiconformal extension, Quasiconformal mappings, Schwarzian derivative, Spirallike functions, Starlike functions, Successive coe cients, Univalent functions. Most of the work in the present thesis is concerned with the class of functions analytic and univalent in the unit disk with the standard normalization. The theory of univalent functions builds a relation between analytic structure and geometric behaviour of complex function theory.