UPPER ESTIMATES OF THE INITIAL COEFFICIENTS OF ANALYTIC FUNCTIONS BELONGING TO A CERTAIN CLASS OF BI-UNIVALENT FUNCTIONS
L. FATUNSIN MODUPE *
Department of Mathematics Programmes, National Mathematical Centre, Abuja, Nigeria.
O. OPOOLA TIMOTHY
Department of Mathematics, Faculty of physical science, University of Ilorin, Kwara-State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this paper, Opoola differential operator, which is a generalization of both Salagean differential operator and Al-Oboudi differential operator is used to define a new subclass of analytic and bi-univalent functions by using quasi-subordination principle. The upper estimates for the first two initial coefficients of functions in the new subclass defined are obtained by means of Ma-Minda functions.
Keywords: Analytic and bi-univalent functions, opoola differential operator, coefficient bounds, Ma-Minda functions