FEKETE-SZEGO PROBLEM FOR SOME SUBCLASSES OF ¨ ANALYTIC FUNCTIONS

In this present investigation, the authors obtain Fekete-Szego's inequality for cer- tain normalized analytic functions f(z) defined on the open unit disk for which zf 0 (z)+z 2 f 00 (z) (1 )f(z)+zf 0(z) ( 0) lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions defined by convolution are given. As a special case of this result, Fekete-Szego's inequality for a class of functions defined through fractional derivatives is obtained. The Motivation of this paper is to give a generalization of the Fekete-Szego inequalities obtained by Srivastava and Mishra .