On the fekete - szego theorem for certain class of analytic functions

Abstract

In this paper we discuss a well known class studied by Ramesha [9] and later by Janteng [5]. Next we extend the class to a wider class of functions J denoted by u/, which are normalized and univalent, in the unit disk D ={ z : 1 z 1 < 1 } satisfying the condition Re(az2J"(Z)+z!'(Z)] > 0, g(z) g(z) O~a< 1, where g E S' (f3), g( z) :;t: 0 is a normalized starlike Junction oj order f3, Jor 0 ~ fJ < l. For J E u/ we shall obtain sharp upper bounds Jor the Fekete-Szego functional 1 a3 - P a221 when p is real.