NEW RESULTS ON A CERTAIN CLASS OF ANALYTIC FUNCTIONS

Folashade Mistura Jimoh1 and Mohammed Umar Faruq2 

1Department of Physical Sciences, Al-Hikmah University, Ilorin, Kwara State, Nigeria

2Department of Computer Science, Kwara State College of Arabic and Islamic Studies, Ilorin, Kwara State, Nigeria

Abstract

The class   is a generalized class of analytic functions that was first studied in [1]. In that paper, it was proved that analytic functions belonging to   are univalent for  . Results on sufficient inclusion criteria for functions to be in   were also establised. In this article, we provide more characterizations for the class   of analytic functions. Specifically, using the well-known Jack’s Lemma and some properties of functions with positive real part, we obtain another sufficient inclusion result for functions to be in  , angular estimates and sufficient conditions for analytic functions   to be strongly starlike of order   and strongly convex functions of order   in the open unit disk are also derived.

Keywords: Analytic functions, univalent functions, angular estimates, strongly starlike and strongly convex functions.