Existence of Solutions to Systems of General Quadratic Functional Equations in $\mathbb{C}^n$
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914144682246144 |
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| author | Ahamed, Molla Basir Mandal, Sanju |
| author_facet | Ahamed, Molla Basir Mandal, Sanju |
| contents | 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 $af^2 + 2αfg + bg^2 + 2βf + 2γg + C=0$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11102 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of Solutions to Systems of General Quadratic Functional Equations in $\mathbb{C}^n$ Ahamed, Molla Basir Mandal, Sanju Complex Variables 39A45, 30D35, 35M30, 32W50 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 $af^2 + 2αfg + bg^2 + 2βf + 2γg + C=0$, 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. |
| title | Existence of Solutions to Systems of General Quadratic Functional Equations in $\mathbb{C}^n$ |
| topic | Complex Variables 39A45, 30D35, 35M30, 32W50 |
| url | https://arxiv.org/abs/2404.11102 |