The Fekete-Szego ̈ Problem for a Generalized Subclass of An- alytic Functions

Abstract. In this present work, the authors obtain Fekete-Szego ̈ inequality for certain normalized analytic function f(z) defined on the open unit disk for which (1−α)z(Dmλ,µf(z))′+αz(Dm+1λ,µ f(z))′ (1−α)Dm λ,µ f(z)+αDm+1 λ,µ f(z) (λ ≥ µ ≥ 0, m ∈ N0, α ≥ 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 Hadamard product (or convolution) are given. As a special case of this result, Fekete-Szego ̈ inequality for a class of func-tions defined through fractional derivatives is obtained. The motivation of this paper is to generalize the Fekete-Szego ̈ inequalities obtained by Srivastava et al., Orhan et al. and Shanmugam et al., by making use of the generalized differential operator Dmλ,µ