Bicomplex Mergelyan's Approximation Theorem

TL;DR

This paper extends classical complex analysis theorems, including Mergelyan's approximation theorem, to the bicomplex setting, broadening the scope of approximation theory in higher-dimensional complex spaces.

Contribution

It introduces and proves bicomplex versions of fundamental theorems like Area, Biebarbach, Koebe Quarter, and Mergelyan's, expanding the theoretical framework.

Findings

Bicomplex Area theorem established

Biebarbach's Theorem proven in bicomplex context

Mergelyan's Approximation Theorem extended to bicomplex functions

Abstract

In this paper we prove Area theorem, Biebarbach`s Theorem, Koebe Quarter Theorem and Mergelyan`s Approximation Theorem in the bicomplex framework.