A Note on Generalized Relative Order (α,β) and Generalized Relative Type (α,β) of a Meromorphic Function with Respect to an Entire Function in the Unit Disc

Abstract

In this paper we introduce the idea of generalized relative order $(\alpha ,\beta )$ and generalized relative type $(\alpha ,\beta )$\ of a meromorphic function with respect to an analytic function in the unit disc $D$ where $\alpha $ and $\beta $ are continuous non-negative on $(-\infty ,+\infty )$ functions. Hence we study some basic properties relating to the sum and product theorems of generalized relative order $(\alpha ,\beta )$ and generalized relative type $(\alpha ,\beta )$\ of a meromorphic function with respect to an analytic function in the unit disc $D$.