Applications of Hadamard Product Techniques To Problems in Univalent Function Theory

Abstract

Abstract : In this thesis we study applications of Hadamard product (convolution) techniques to problems in univalent function theory. Proofs of several conjectures made by different researchers are discussed. Using the results of Ruscheweyh and Sheil-Small developed in connection with their proof of Pólya-Schoenberg conjecture, we exploit the strengths and properties of various convolution operators. A unified approach to the study of certain properties of existing and new subclasses of univalent analytic functions is also given by introducing and studying the classes E7(φ, ψ,α,β) and Ε(φ, ψ,α,β). The approach not only generalize corresponding known results but also give an analogous study for several other subclasses of univalent analytic functions.