Characterization and Stability of Multi-Euler-Lagrange -Jensen- Cubic Functional Equations

Abstract

The paper aims to investigate an alternative form of multi-Euler-Lagrange-cubic mappings. We provide a characterization of multi-Euler-Lagrange cubic mappings and multi-Euler-Lagrange-Jensen-cubic mappings by unifying the corresponding systems of equations into a single defining equation. We investigate the Hyers-Ulam stability for multi-Euler-Lagrange-Jensen- cubic mappings by applying a fixed-point method in Banach spaces. Also, we deduce several other results corresponding to well-known stability results, and provide a suitable counterexample to demonstrate a failure case of stability.