On some inequalities concerning generalized (α,β) relative order and generalized (α,β) relative type of entire function with respect to an entire function

Abstract

In this paper, we intend to find out some inequalities relating to generalized (α ,β) relative order, generalized (α ,β) relative type and generalized (α ,β) relative weak type of an entire function f with respect to an entire function g when generalized (γ ,β) relative order, generalized (γ ,β) relative type and generalized (γ ,β) relative weak type of f with respect to another entire function h and generalized (γ ,α) relative order, generalized (γ ,α) relative type and generalized (γ ,α) relative weak type of g with respect to h are given, where α , β and γ are continuous non-negative slowly increasing functions defined on (−∞,+∞) . Mathematics subject classification (2020): 30D20, 30D30, 30D35.