In this study, we utilize the direct method (Hyers approach) to examine the refined stability of the additive, quartic, and sextic functional equations in modular spaces with and without the ∆2-condition. We also use the direct approach to discuss the Ulam stability in 2-Banach spaces. Ultimately, we ensure that stability of above equations does not hold in a particular scenario by utilizing appropriate counter-examples.
- 2-Banach space
- modular space
- quartic and sextic functional equations
- refined stability