Notes on Harmonic Functions for which the second Dilatation is α - spiral

Abstract

In this study, we consider, f = h + (g) over bar harmonic functions in the unit disc D. By applying S. S. Miller and P. M. Mocanu result, we obtain a new subclass of harmonic functions, such as S-HPST*(alpha, beta) We introduce this new class as defined in the following form, S-HPST*(alpha, beta) = {f = h(z) + <(g(z))over bar>vertical bar f is an element of S-H, h(z) is an element of S* , Re (e(i alpha)g '(z)/h '(z)) > beta,vertical bar alpha vertical bar < pi/2,0 <= beta < (0.1), We also use subordination principle, study on distortion theorems, some numerical examples and coefficient inequalities of this class.