Coefficient inequalities for certain classes of sakaguchi - type harmonic functions

Abstract

Let S H (alpha, s, t) be the class of normalized harmonic functions f = h + g defined in the open unit disk satisfyingRe{(s-t)(zh'(z)-zg'(z) / h(sz)-h(tz)+g(sz)-g(tz)} > alphafor complex numbers s, t with s not equal t and for ff (0 <= alpha < 1). The main object of this paper is to obtain a necessary and sufficient convolution characterization and a sufficient coefficient condition for the class SH (alpha, s, t). Also, distortion bounds for the function f satisfying the coefficient condition are obtained.