Fixed points and approximately octic mappings in non-Archimedean 2-normed spaces

Abstract

Using the fixed point method, we investigate the Hyers-Ulam stability of the system of additive-cubic-quartic functional equations with constant coefficients in non-Archimedean 2-normed spaces. Also, we give an example to show that some results in the stability of functional equations in (Archimedean) normed spaces are not valid in non-Archimedean normed spaces. MSC: 39B82; 46S10; 39B52; 47S10; 47H10

On Ulam Stability of Functional Equations in 2-Normed Spaces—A Survey II

“…In this paper, we complement the content of [23], where the (less complicated) results from [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] have been surveyed. Here, we present and discuss the (more involved) outcomes on Ulam stability in 2-normed spaces provided in [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58].…”

Stability and nonstability of octadecic functional equation in multi-normed spaces

“…for all x ∈ X . Since the past few decades several stability problems of functional equations have been investigated [1,2,[5][6][7]11,12,14,19]. Xu et al [20] proved the general solution and the stability of the quintic functional equation…”

On the Stability of a k-Cubic Functional Equation in Intuitionistic Fuzzy n-Normed Spaces

“…Motivated by the theory of n-normed linear space [7,8,11,12,18,19] and fuzzy normed linear space [2][3][4][5][6] the notions of fuzzy n-normed linear space [16] and intuitionistic fuzzy n-normed linear space [17,27] were developed. A stability problem of a functional equation was first posed by Ulam [26] which was answered by Hyers [9] and then generalized by Aoki [1] and Rassias [23] for additive mappings and linear mappings, respectively.…”