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

Author

Listed:
  • 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
    Research and Development Center, 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)

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.

Suggested Citation

  • Jagjeet Jakhar & Shalu Sharma & Jyotsana Jakhar & Majeed A. Yousif & Pshtiwan Othman Mohammed & Alina Alb Lupas & Nejmeddine Chorfi, 2024. "Orthogonal Stability and Solution of a Three-Variable Functional Equation in Extended Banach Spaces," Mathematics, MDPI, vol. 12(18), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:18:p:2868-:d:1478564
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