ON COMPARATIVE GROWTH RELATIONSHIP OF ITERATED ENTIRE FUNCTIONS FROM THE VIEWPOINT OF SLOWLY CHANGING

Abstract

A positive continuous function L= L(r) is called slowly if L(ar) ~ L(r) as r͢-∞   for every positive constant “a”. Lakshminarasimhan [14] introduced the idea of the functions of L-bounded index. Later Lahiri and Bhattacharjee [16] worked on the entire functions (i.e., functions analytic in the finite complex plane) of L-bounded index and of non uniform L-bounded index. The growth of an entire function f with respect to another entire function g is de.ned as the ratio of their maximum moduli for sufficiently large values of r. The same may be de.ned in terms of maximum terms as well as Nevanlinna’s characteristic functions of entire functions. In this paper we would like to investigate some comparative growth analysis of iterated entire functions (as de.ned by Lahiri and Banerjee [15]) on the basis of their maximum terms, maximum moduli and Nevanlinna.s characteristic functions and obtain some powerful results with a scope of further research in the concerned area.