Estimation of specific class, in the unit disc holomorphic functions

Abstract

Let f be in the unit Disk holomorphic function with Re (f (z) > 0 and f (0) =1. For this type of function, we studied the boundary estimate values in the unit Disk and obtained the best estimation. The Schwarz lemma, the Schwarz-pick lemma, and the Green function for a unit Disk are all examples of lemmas. The equality of f and g in unit disc restricted holomorphic functions under specific conditions, as well as the relationships between the Green function for a unit disc and the Schwarz lemma, are useful tools in this paper to achieve the goal. Moreover we have obtained that f is, subordinate to 1+Z-1-Z.