Ulam Stability Results of Functional Equations in Modular Spaces and 2-Banach Spaces

Abstract

In this work, we investigate the refined stability of the additive, quartic, and quintic functional equations in modular spaces with and without the Δ2-condition using the direct method (Hyers method). We also examine Ulam stability in 2-Banach space using the direct method. Additionally, using a suitable counterexample, we eventually demonstrate that the stability of these equations fails in a certain case.

Keywords

• quartic and quintic functional equations
• modular spaces
• 2-Banach spaces
• refined stability