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2021•Advances in Difference EquationsOpen access

Characterization and stability analysis of advanced multi-quadratic functional equations

Abasalt Bodaghi, Hossein Moshtagh, Hemen Dutta

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Abstract

Abstract In this paper, we introduce a new quadratic functional equation and, motivated by this equation, we investigaten-variables mappings which are quadratic in each variable. We show that such mappings can be unified as an equation, namely, multi-quadratic functional equation. We also apply a fixed point technique to study the stability for the multi-quadratic functional equations. Furthermore, we present an example and a few corollaries corresponding to the stability and hyperstability outcomes.

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What this paper is about

Abstract In this paper, we introduce a new quadratic functional equation and, motivated by this equation, we investigaten-variables mappings which are quadratic in each variable. We show that such mappings can be unified as an equation, namely, multi-quadratic functional equation. We also apply a fixed point technique to study the stability for the multi-quadratic functional equations. Furthermore, we present an example and a few corollaries corresponding to the stability and hyperstability outcomes.

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Available abstract

Abstract In this paper, we introduce a new quadratic functional equation and, motivated by this equation, we investigaten-variables mappings which are quadratic in each variable. We show that such mappings can be unified as an equation, namely, multi-quadratic functional equation. We also apply a fixed point technique to study the stability for the multi-quadratic functional equations. Furthermore, we present an example and a few corollaries corresponding to the stability and hyperstability outcomes.

Key concepts: Quadratic equation, Functional equation, Mathematics, Partial differential equation, Stability (learning theory), Ordinary differential equation, Characterization (materials science), Applied mathematics

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