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arXiv · 2404.11102

Existence of Solutions to Systems of General Quadratic Functional Equations in $\mathbb{C}^n$

Molla Basir Ahamed·Sanju Mandal
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Abstract

The main objective of this study is to investigate the existence and forms of solutions of systems of general quadratic functional equations in $\mathbb{C}^n$. By utilizing Nevanlinna theory in $\mathbb{C}^n$, we explore the existence and form of solutions for the several systems of general quadratic difference and partial differential-difference equations of the form $af^2 + 2\alpha fg + bg^2 + 2\beta f + 2\gamma g + C=0$, where $f$ and $g$ are non-constant meromorphic functions in $\mathbb{C}^n$. The obtained results in this article are improvements and generalizations of several results from [\textit{RACSAM}, \textbf{116}(8) (2022)]. Furthermore, appropriate remarks and illustrative examples are provided to validate and demonstrate the applicability of the obtained results concerning the existence and forms of solutions for such systems of equations.

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Molla Basir Ahamed, Sanju Mandal. 2024-04-17. Existence of Solutions to Systems of General Quadratic Functional Equations in $\mathbb{C}^n$. https://arxiv.org/abs/2404.11102

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