Bi-concave functions involving a differential operator

Abstract

The purpose of the present paper is to introduce a class (D lambda,delta C0)-C-k,alpha(beta) of bi-concave functions defined by a differential operator. We find estimates on the Taylor-Maclaurin coefficients vertical bar a(2)vertical bar and vertical bar a(3)vertical bar for functions in this class. Several consequences of these results are also pointed out in the form of corollaries.