THE FEKETE-SZEGÖ PROBLEM FOR SUBCLASSES OF ANALYTIC FUNCTIONS ASSOCIATED WITH DIFFERENTIAL OPERATOR

Abstract

The aim of this paper is to determine the Fekete-Szegö inequality for the class 〖 M〗_(λ_1,λ_2,l,d)^(n,m) (∅) of normalized analytic functions f(z) defined on the open unit disk for which z(D_(λ_1,λ_2,l,d)^(n,m) f (z))'/(D_(λ_1,λ_2,l,d)^(n,m) f (z)) lies in a region starlike with respect to 1 and symmetric with respect to the real axis by using the differential operator D_(λ_1,λ_2,l,d)^(n,m) f(z) given by authors Oshah and Darus. As a special case of this result, Fekete-Szegö inequality for a class of functions that is defined by fractional derivatives is to be obtained too.