BICOMPLEX AND MULTICOMPLEX ANALOGUE OF FEW THEOREMS ON NORMAL FAMILY OF FUNCTIONS
By
Sanjib Kumar Datta
Department of Mathematics, University of Kalyani, P.O.: Kalyani, Dist: Nadia, West Bengal, India-741235 Email: sanjibdatta05@gmail.com
(Received: October 11, 2025; Revised: November 24, 2025; Accepted: December 02, 2025)
DOI: https://doi.org/10.58250/jnanabha.2025.55227
Abstract
This paper develops bicomplex and multicomplex analogues of fundamental theorems in complex analysis including Arzel`a-Ascoli theorem, Montels theorems (holomorphic and meromorphic), Martys theorem, Riemann mapping theorem and Hurwitz’s theorem. Each result is rigorously adapted to the bicomplex and multicomplex framework using the idempotent decomposition and classical componentwise reduction.
2020 Mathematical Sciences Classification: 30G35, 30D45, 32A30, 32A55, 32H02.
Keywords and Phrases: Bicomplex analysis; Multicomplex analysis; Normal families; Arzel`aAscoli theorem; Montel’s theorem; Martys criterion; Hurwitz’s theorem; Riemann mapping theorem; Holomorphic and meromorphic functions.