A Study of Quasi-Normal Families of Bicomplex Holomorphic Functions

Khan TA, Gupta J and Kumar R

Published on: 2023-11-03

Abstract

In this paper, we introduced the concept of bicomplex -point and bicomplex -point to obtain -sequence and -Sequence of holomorphic functions on bicomplex domain. Further, we have extended fundamental ingleb Decomposition Theorem for -Sequence and proved some basic results of -Sequence on bicomplex setting. Moreover, we have defined the quasi-normal family in bicomplex setting by using -Sequences and proved some basic result of quasi-normal families of holomorphic functions on bicomplex domain.

Keywords

Bicomplex numbers; Bicomplex holomorphic functions; Quasi-normal families; C_0-point; C_1-point; C_0- sequence and C_1-sequence

Introduction

The concept of quasi normal families of holomorphic functions was introduced by the French mathematician Arnaud Denjoy in 1929. The notion of quasi normality was motivated by the study of the behaviour of sequences of 1 holomorphic functions in certain function spaces, and was initially developed as a weaker alternative to normality. Since its introduction, the concept of quasi normality has become an important tool in complex analysis, particularly in the study of the geometric properties of domains in the complex plane.