A fixed point approach to the stability of a quadratic functional equation in modular spaces without $Δ₂$ conditions: Real Functions and Algebra

Strany: 47 - 64

Jazyk: eng

In this paper, we investigate the Hyers-Ulam-Rassias stability property of a quadratic functional equation. The even and odd cases for the corresponding function are treated separately before combining them into a single stability result. The study is undertaken in a relatively new structure of modular spaces. The theorems are deduced without using the familiar $Δ₂$-property of that space. This implicated the proofs. In the proofs, a fixed point methodology is used for which a modular space version of Banach contraction mapping principle is utilized. Several corollaries and an illustrative example are provided.

ISO 690:

Saha, P., Kayal, N. C., Choudhury, B. S., Dutta, S., Mondal, S. P. 2024. A fixed point approach to the stability of a quadratic functional equation in modular spaces without $Δ₂$ conditions: Real Functions and Algebra. In Tatra Mountains Mathematical Publications, vol. 86, no.1, pp. 47-64. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2024-0016

APA:

Saha, P., Kayal, N. C., Choudhury, B. S., Dutta, S., Mondal, S. P. (2024). A fixed point approach to the stability of a quadratic functional equation in modular spaces without $Δ₂$ conditions: Real Functions and Algebra. Tatra Mountains Mathematical Publications, 86(1), 47-64. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2024-0016

Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava

https://creativecommons.org/licenses/by-nc-nd/4.0/