Abstract

In this paper, we intend to find out some inequalities of generalized relative order $(\alpha ,\beta )$, generalized relative type $(\alpha ,\beta )$ and generalized relative weak type $(\alpha,\beta )$ of a meromorphic function $f$ with respect to an entire function $g$ when generalized relative order $(\gamma ,\beta ),$ generalized relative type $(\gamma ,\beta )$ and generalized relative weak type $(\gamma ,\beta )$ of $f$ and generalized relative order $(\gamma ,\alpha )$, generalized relative type $(\gamma ,\alpha )$ and generalized relative weak type $(\gamma ,\alpha )$ of $g$ with respect another entire function $h$ are given, where $\alpha ,$ $\beta ,\gamma $ are slowly increasing functions.

Keywords and Phrases

Entire function, meromorphic function, growth, generalized relative order $(\alpha ,\beta )$, generalized relative type $(\alpha ,\beta )$.

A.M.S. subject classification

30D35, 30D30, 30D20.

.....