Bi-concave functions involving a differential operator

Abstract

The purpose of the present paper is to introduce a class $\boldsymbol{D}% _{\lambda ,\delta }^{k,\alpha }C_{0}(\beta )$ of bi-concave functions defined by a differential operator. We find estimates on the Taylor-Maclaurin coefficients $\left\vert a_{2}\right\vert $ and $\left\vert a_{3}\right\vert $ for functions in this class. Several consequences of these results are also pointed out in the form of corollaries.