A Fixed Point Approach to the Stability of a Quadratic Functional Equation in Modular Spaces Without Δ2-Conditions

Parbati Saha; Nabin C. Kayal; Binayak S. Choudhury; Santu Dutta; Sankar Prasad Mondal

doi:10.2478/tmmp-2024-0016

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A Fixed Point Approach to the Stability of a Quadratic Functional Equation in Modular Spaces Without Δ2-Conditions

Tatra Mountains Mathematical Publications

Volume 86 (2024): Issue 1 (September 2024)

By: Parbati Saha, Nabin C. Kayal, Binayak S. Choudhury, Santu Dutta and Sankar Prasad Mondal

Open Access

|Oct 2024

Abstract

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 complicated 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.

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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2024-0016 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 47 - 64

Submitted on: Apr 15, 2023

Accepted on: Nov 11, 2023

Published on: Oct 20, 2024

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

quadratic functional equation,

Hyers-Ulam-Rassias stability,

Related subjects:

© 2024 Parbati Saha, Nabin C. Kayal, Binayak S. Choudhury, Santu Dutta, Sankar Prasad Mondal, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 86 (2024): Issue 1 (September 2024)