Hyperstability of cubic functional equation in ultrametric spaces

Abstract

In this paper, we present the hyperstability results of cubic functional equations in ultrametric Banach spaces.

Hyperstability of the k -Cubic Functional Equation in Non-Archimedean Banach Spaces

“…is shows that ( 18) holds for n � r + 1. Now, we can conclude that inequality (18) holds for all n ∈ N 0 . From (18), we obtain…”

“…Quite often, hyperstability is confused with superstability, which also admits bounded functions. Numerous papers on this subject have been published, and we refer, for example, to [3,[12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. roughout this paper, N stands for the set of all positive integers and N m 0 , the set of integers greater than or equal m 0 , R + ≔ [0, ∞), and we use the notation X 0 for the set X∖ 0 { }.…”