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

Abstract

Using the fixed point approach, we investigate a general hyperstability results for the following k -cubic functional equations f k x + y + f k x − y = k f x + y + k f x − y + 2 k k 2 − 1 f x , where k is a fixed positive integer ≥ 2 , in ultrametric Banach spaces.

Orthogonally Fixed Points and (m, m)‐Hom‐Derivation Equations

“…By using the concept of orthogonal sets, Bahraini et al [22] proved the generalization of the Diaz-Margolis [23] fixed point theorem on these sets. e study on orthogonal sets has been done by several authors (for example, see [24][25][26]).…”