Quartic Functional Equation: Ulam-Type Stability in (β, p)-Banach Space and Non-Archimedean β-Normed Space

In this study, we use the alternative fixed-point approach and the direct method to examine the generalized Hyers-Ulam stability of the quartic functional equation g(u + mv) + g(u - mv) = 2(m - 1) (7m - 9)g(u) + 2(m(2) - 1)m(2)g(v) - (m - 1)(2) g(2u) + m(2){g(u + v) + g(u - v)}, with a fixed positive integer m/ge2 in the context of (beta, p)-Banach space. In non-Archimedean beta-normed space, we also verify Hyers-Ulam stability for the quartic functional equation stated. Many of the findings in the literature are improved and generalized by our findings.

Automated summary

In this study, we use the alternative fixed-point approach and the direct method to examine the generalized Hyers-Ulam stability of a quartic functional equation in the context of (beta, p)-Banach space. We also verify the Hyers-Ulam stability for the quartic functional equation in non-Archimedean beta-normed space. Our findings improve and generalize many of the previous findings in the literature.