Tamilvanan, KandhasamyAlkhaldi, Ali H.Jakhar, JyotsanaChugh, RenuJakhar, JagjeetRassias, John, Michael2023-05-052023-05-052023http://hdl.handle.net/123456789/1154In this work, we investigate the refined stability of the additive, quartic, and quintic functional equations in modular spaces with and without the D2-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.enquartic and quintic functional equations; modular spaces; 2-Banach spaces; refined stabilityArticle