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

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

doi:10.2478/tmmp-2024-0016

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

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