Comparative Results on Stability Analysis for Three Dimensional Functional Equations

Authors

  • Jagjeet Jakhar Department of Mathematics, Central University of Haryana, Jant-Pali, Mahendergarh, 123031, India
  • Dumitru Baleanu Department of Computer Science and Mathematics, Lebanese American University, Beirut 11022801, Lebanon
  • Shalu Sharma Department of Mathematics, Central University of Haryana, Jant-Pali, Mahendergarh, 123031, India
  • Majeed A. Yousif Department of Mathematics, College of Education, University of Zakho, Zakho 42002, Iraq
  • Jyotsana Jakhar Department of Mathematics, Pandit Neki Ram Sharma Government College, Rohtak, Haryana, 123031, India
  • Nejmeddine Chorfi Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
  • Pshtiwan Othman Mohammed Department of Mathematics, College of Education, University of Sulaimani, Sulaymaniyah 46001, Iraq

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.6098

Keywords:

Functional equation, Stability, $(n,\beta)$-normed space, Random normed space

Abstract

This study investigates the stability of a three-dimensional cubic functional equation within several mathematical frameworks, including $(n, \beta)$-normed spaces, non-Archimedean $(n, \beta)$-normed spaces, and random normed spaces. The theoretical stability results are validated through experimental approaches, offering practical insight into the behavior of these functional equations. A comparative analysis is provided, highlighting differences in stability dynamics across the various spaces. Notably, the introduction of $(n, \beta)$-normed spaces and their non-Archimedean counterparts presents a novel framework for analyzing stability, while the inclusion of random normed spaces adds a stochastic dimension to the analysis. The experimental validation further strengthens the practical application of the stability results, distinguishing this study from traditional approaches.

Author Biography

  • Pshtiwan Othman Mohammed, Department of Mathematics, College of Education, University of Sulaimani, Sulaymaniyah 46001, Iraq

    Associate member of section of Mathematics, International Telematic University Uninettuno, Corso Vittorio
    Emanuele II, 39, 00186 Roma, Italy 

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Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Mathematical Analysis

License

Copyright (c) 2025 Jagjeet Jakhar, Dumitru Baleanu, Shalu Sharma, Majeed A. Yousif, Jyotsana Jakhar, Nejmeddine Chorfi, Pshtiwan Othman Mohammed

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How to Cite

Comparative Results on Stability Analysis for Three Dimensional Functional Equations. (2025). European Journal of Pure and Applied Mathematics, 18(2), 6098. https://doi.org/10.29020/nybg.ejpam.v18i2.6098