Bohr�Rogosinski Inequalities for Certain Fully Starlike Harmonic Mappings

Abstract

Let H be the class of complex-valued harmonic mappings f= h+ g� defined in the unit disk D, where h and g are analytic functions in D with h(0) = 0 = h?(0) - 1 and g(0) = 0 and H= { f= h+ g� ? H: g?(0) = 0 } and PH0(M):={f=h+g�?H0:Re(zh?(z))>-M+|zg?(z)|,z?D,M>0}. Functions in the class PH0(M) are known to be fully starlike univalent functions for 0 < M< 1 / log 4. In this paper, we obtain the sharp Bohr�Rogosinski type inequality and improved Bohr inequality and the corresponding Bohr radius for the class PH0(M). � 2022, The Author(s), under exclusive licence to Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia.