HYPERSTABILITY ANALYSIS FOR APOLLONIUS FUNCTIONAL EQUATIONS WITH FIXED POINT THEORY BASED ON A QUASI SPACE

Jagjeet Jakhar; Shalu Sharma; Majeed Ahmad Yousif; Jyotsana Jakhar; Meraa Arab; Dumitru Baleanu; Pshtiwan Othman Mohammed

doi:10.11948/20250136

2026 Volume 16 Issue 4

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Jagjeet Jakhar, Shalu Sharma, Majeed Ahmad Yousif, Jyotsana Jakhar, Meraa Arab, Dumitru Baleanu, Pshtiwan Othman Mohammed. HYPERSTABILITY ANALYSIS FOR APOLLONIUS FUNCTIONAL EQUATIONS WITH FIXED POINT THEORY BASED ON A QUASI SPACE[J]. Journal of Applied Analysis & Computation, 2026, 16(4): 2172-2189. doi: 10.11948/20250136

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Jagjeet Jakhar, Shalu Sharma, Majeed Ahmad Yousif, Jyotsana Jakhar, Meraa Arab, Dumitru Baleanu, Pshtiwan Othman Mohammed. HYPERSTABILITY ANALYSIS FOR APOLLONIUS FUNCTIONAL EQUATIONS WITH FIXED POINT THEORY BASED ON A QUASI SPACE[J]. Journal of Applied Analysis & Computation, 2026, 16(4): 2172-2189. doi: 10.11948/20250136

HYPERSTABILITY ANALYSIS FOR APOLLONIUS FUNCTIONAL EQUATIONS WITH FIXED POINT THEORY BASED ON A QUASI SPACE

1.
Department of Mathematics, Central University of Haryana, Jant-Pali, Mahendergarh 123031, India
2.
Department of Mathematics, College of Education, University of Zakho, Zakho 42002, Iraq
3.
Department of Mathematics, Pt. NRS Govt. College, Rohtak, Haryana 123031, India
4.
Department of Mathematics and Statistics, College of Science, King Faisal University, Al Ahsa 31982, Saudi Arabia
5.
Department of Computer Science and Mathematics, Lebanese American University, Beirut 11022801, Lebanon
6.
Department of Mathematics, College of Education, University of Sulaimani, Sulaymaniyah 46001, Iraq
7.
Department of Computer Engineering, Biruni University, 34010 Istanbul, Turkey
8.
Associate member of Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele Ⅱ, 39, 00186 Roma, Italy

Author Bio: Email: jagjeet@cuh.ac.in(J. Jakhar); Email: shalu211940@cuh.ac.in(S. Sharma); Email: majeed.yousif@uoz.edu.krd(M. A. Yousif); Email: dahiya.jyotsana.j@gmail.com(J. Jakhar); Email: dumitru.baleanu@lau.edu.lb(D. Baleanu)
Corresponding authors: Email: marab@kfu.edu.sa(M. Arab); Email: pshtiwansangawi@gmail.com(P. O. Mohammed)

Abstract

Abstract

This paper investigates a fixed-point theorem within the framework of quasi-(m, β)-normed spaces, extending the results of Brzdek [5] and El-Fassi [6] to a more generalized setting. The extension is utilized to study the hyperstability of Apollonius-type functional equations, emphasizing the role of inequalities in stability analysis. By employing advanced fixed-point methods, we provide a comprehensive framework that highlights the interplay between inequalities and stability phenomena in functional equations. These findings contribute to the growing body of research on inequalities in functional analysis and their applications in diverse mathematical contexts.
- Apollonius type functional equation /
- hyperstability /
- (m, β)-normed space /
- fixed point theorem
MSC: 47H10, 46A16, 39B82

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References

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