Hadamard Product of a Class of Holomorphic Functions with an Arbitrary Fixed Point

Abstract

Hadamard product of holomorphic function is simply entry wise multiplication of two functions f and g in . The Hadamard products of two functions have one thing in common that is, it involves the origin. Irrespective of the factors of the Hadamard product either power series or holomorphic functions, the open sets on which they are examined contain the origin. The aim of this study, therefore, is to investigate on the properties of Hadamard product for a class of holomorphic functions with an arbitrary fixed point. The concept of Hadamard product, Cauchy-Schwartz, holomorphic functions, Ruscheweyh differential operators, and Nevanlinna’s theorem are employed in this study. This study generalized the coefficient inequalities for starlike and convex functions of exponential order  with an arbitrary fixed point using Ruscheweyh derivative. This study further provides an additional inequality and Hadamard product for a class of holomorphic functions with an arbitrary fixed point. It is concluded that Ruscheweyh derivative is an effective tool in the generalization of Hadamard product for a class of holomorphic functions with an arbitrary fixed point.