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 () and Nejmeddine Chorfi
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Jagjeet Jakhar: Department of Mathematics, Central University of Haryana, Mahendergarh 123031, Haryana, India
Shalu Sharma: Department of Mathematics, Central University of Haryana, Mahendergarh 123031, Haryana, India
Jyotsana Jakhar: Department of Mathematics, M.D. University, Rohtak 124001, Haryana, India
Majeed A. Yousif: Department of Mathematics, College of Education, University of Zakho, Duhok 42001, Iraq
Pshtiwan Othman Mohammed: Department of Mathematics, College of Education, University of Sulaimani, Sulaymaniyah 46001, Iraq
Alina Alb Lupas: Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania
Nejmeddine Chorfi: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Mathematics, 2024, vol. 12, issue 18, 1-15

Abstract: 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.

Keywords: functional equations; multi-Banach space; quasi-Banach space; stability; orthogonal space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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