On Fermat-Type Binomial Equations Involving Differential Difference Form in Higher Dimensional Complex Plane

This paper is focused to find the potential solutions of a binomial Fermat type functional equation in C2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {C}}<^>2$$\end{document} where the equation involves operators formed by linear combinations of functions, shifts, and derivatives as it allows for a more comprehensive understanding of the underlying structures and relationships. Our approach is the first to unify the treatment of the function and its two important variants within a common framework to analyze the impact of the operator on the solutions of the Fermat type functional equation in two dimensional complex field. In our another attempt, for a specific subclass of the combination of the operators, we have been able to extend our result for n dimensional complex plane.