Stability of an AQCQ functional equation in non-Archimedean (n, β)-normed spaces

Abstract

In this paper, we adopt direct method to prove the Hyers-Ulam-Rassias stability of an additivequadratic-cubic-quartic functional equation$$f(x + 2y) + f(x - 2y) = 4f(x + y) + 4f(x - y) - 6f(x) + f(2y) + f( - 2y) - 4f(y) - 4f( - y)$$in non-Archimedean (n, β)-normed spaces.

Stability of Davison functional equation with n - variables over non-Archimedean ( n , β ) normed spaces

“…Thereafter, Abdollahpour [2,1] obtained the Hyers-Ulam stability of differential equations. In 2019, Park and Rassias [30] discussed additive functional equations and partial multipliers in C*-algebras as well as Liu et al [27] gave stability of an AQCQ functional equation in NAnβNS. Recently, Najati and Sahoo [29] discussed two Pexiderized functional equation of Davison type in 2023.…”

Hyers-Ulam Stability of Quadratic Functional Equation Based on Fixed Point Technique in Banach Spaces and Non-Archimedean Banach Spaces

“…Xiuzhong Yang [17] examined the Hyers-Ulam-Rassias stability of an additivequadratic-cubic-quartic functional equation in non-Archimedean (n, β)-normed spaces. Anurak Thanyacharoen [18,19] proved the generalized Hyers-Ulam-Rassias stability for the following composite functional equation:…”

A Criterion for the Existence of the Unique Periodic Solution of One-Dimensional Periodic Differential Equation

“…As we all know, the existence, uniqueness, and stability of periodic solutions of differential equations have always been an important research hotspot in the field of differential equations (see [10][11][12][13][14][15][16][17][18][19][20]). However, the above literatures are basically about the study of periodic solutions of specific equations, rather than the study of general differential equations.…”