Stability of general quadratic Euler–Lagrange functional equations in modular spaces: a fixed point approach

In this paper, we establish a result on the Hyers–Ulam–Rassias stability of the Euler–Lagrange functional equation. The work presented here is in the framework of modular spaces. We obtain our results by applying a fixed point theorem. Moreover, we do not use the $\Delta_\alpha$-condition of modular spaces in the proofs of our theorems, which introduces additional complications in establishing stability. We also provide some corollaries and an illustrative example. Apart from its main objective of obtaining a stability result, the present paper also demonstrates how fixed point methods are applicable in modular spaces.