Mathematics (Sep 2024)

Orthogonal Stability and Solution of a Three-Variable Functional Equation in Extended Banach Spaces

  • Jagjeet Jakhar,
  • Shalu Sharma,
  • Jyotsana Jakhar,
  • Majeed A. Yousif,
  • Pshtiwan Othman Mohammed,
  • Alina Alb Lupas,
  • Nejmeddine Chorfi

DOI
https://doi.org/10.3390/math12182868
Journal volume & issue
Vol. 12, no. 18
p. 2868

Abstract

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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.

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