On fekete-szegö problems for a subclass of analytic functions

Abstract

The aim of this paper is to determine the Fekete-Szegö inequalities for a normalised analytic function f (z) defined on the open unit disc for which z(Dλ1,λ2 ,δ m,b f (z))′ / (Dλ1,λ2 ,δ m,b f (z)),δ ,m,b ∈N0 ,λ2 ≥ λ1 ≥ 0 lies in a region starlike with respect to 1 and it is symmetric with respect to the real axis by using the operator Dλ1,λ2 ,δ m,b f (z) given recently by the authors. As a special case of this result, Fekete-Szegö inequality for a class of functions defined by fractional derivatives is also obtained.