Fekete-Szego Problem for a Generalized Subclass of Analytic Functions

In this present work, the authors obtain Fekete-Szeg " o inequality for certain normalized analytic function f (z) defined on the open unit disk for which lambda beta z(3) (L(a; c) f (z))''' + (2 lambda beta+lambda-beta)z (2) (L (a; c) f (z))'' + z (L (a; c) f (z))'/ lambda beta z(2) (L(a; c) f (z))'' + (lambda-beta) z (L (a; c) f (z))' + (1-lambda+ beta)(L(a; c) f (z)) (0 <= beta <=lambda <= 1) 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 functions defined through fractional derivatives are obtained.