A critical investigation of various subclasses of functions whose real part is bounded

Abstract

In this paper we investigate various subclasses of univalent analytic functions. We find that many of the subclasses introduced in the recent years are no more new and infact coincide with the class due to Jakubowski. We further study the generalised Jakubowski class of univalent functions and obtain a representational formula and use it in deriving the coefficient relations for this class