Differential Operators and Fekete-Szego Problem

In this paper, a sharp upper bound for the functional vertical bar a3 - mu a(2)(2)vertical bar for functions f is an element of A in the class of function S* (Phi(1), Phi(2), phi) which we call it as the class of Phi(2) - like functions of type Phi(1). Also certain applications of the main result for a class of functions defined by convolution are given. As a special case of the result, the Fekete-Szego inequality for a class of functions defined through fractional derivatives is obtained. The objective of this paper is to give a generalization of the earlier Fekete-Szego inequalities.