SOME RESULTS IN CONNECTION WITH SUM AND PRODUCT THEOREMS RELATED TO GENERALIZED RELATIVE ORDER $(\alpha ,\beta )$ AND GENERALIZED RELATIVE TYPE $(\alpha,\beta )$ OF ENTIRE FUNCTIONS IN THE UNIT DISC

Abstract

Orders and types of entire functions have been actively investigated by many authors. In this paper, we investigate some basic properties in connection with sum and product of generalized relative order $(\alpha ,\beta )$, generalized relative type $(\alpha ,\beta )$ and generalized relative weak type $(\alpha ,\beta )$ of entire functions in the unit disc $D$ with respect to another entire function where $\alpha ,$ $\beta $ are continuous non-negative functions on $(-\infty ,+\infty )$.