GROWTH PROPERTIES OF AN ANALYTIC FUNCTION OF SEVERAL COMPLEX VARIABLES IN THE UNIT POLYDISC ON THE BASIS OF RELATIVE ORDER
By
Suraj Bhan, Jyoti Rani and Anupma Rastogi
Department of Mathematics and Astronomy, University of Lucknow, Lucknow, Uttar Pradesh, India-226007 Email: sb992751@gmail.com, gaytriarya100@gmail.com, anupmarastogi13121993@gmail.com
(Received: November 06, 2024; In format: January 08, 2025; Revised: August 17, 2025; Accepted: October 22, 2025)
DOI: https://doi.org/10.58250/jnanabha.2025.55216
Abstract
In this paper, we study some comparative growth properties of composite analytic function of several complex variables, on the basis of relative order and relative lower order of an entire function with respect to an analytic function in the unit polydisc. Here we introduce some definitions related to relative order and relative lower order in terms of central index and study them critically.
2020 Mathematical Sciences Classification: 32A05, 32C15
Keywords and Phrases: Analytic function in the unit polydisc, maximum term, several complex variables, maximum modulus, composition, generalized relative order, generalized relative L order, generalized relative L ∗ order, central index.