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Orthogonal Stability and Solution of a Three-Variable Functional Equation in Extended Banach Spaces
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This manuscript introduces a novel three-variable cubic functional equation and derives its general solution. Employing both the direct and fixed-point methods, we investigate the orthogonal stability of this equation within the frameworks of quasi-β-Banach spaces and multi-Banach spaces. Additionally, the study explores the stability of the equation in various extended Banach spaces and provides a specific example illustrating the absence of stability in certain cases.
Title: Orthogonal Stability and Solution of a Three-Variable Functional Equation in Extended Banach Spaces
Description:
This manuscript introduces a novel three-variable cubic functional equation and derives its general solution.
Employing both the direct and fixed-point methods, we investigate the orthogonal stability of this equation within the frameworks of quasi-β-Banach spaces and multi-Banach spaces.
Additionally, the study explores the stability of the equation in various extended Banach spaces and provides a specific example illustrating the absence of stability in certain cases.
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