Orthogonal Stability of an Additive-quartic Functional Equation in Non-Archimedean Spaces

Abstract

Using fixed point method, we prove the Hyers-Ulam stability of the orthogonally additivequartic functional equationfor all x, y with x ⊥ y, in non-Archimedean Banach spaces. Here ⊥ is the orthogonality in the sense of Rätz.

Cauchy-Jensen additive mappings in quasi-Banach algebras and its applications

“…Gȃvruta [7] generalized the Rassias' result. The stability problems of several functional equations have been extensively investigated by a number of authors and there are many interesting results concerning this problem (see [5,6], [9,10], [12]- [19], [21]- [23], [28]- [30]). …”

On the Stability of Hyers Orthogonality Functional Equations in Non-Archimedean Spaces

“…Kang [10] explored the stability of the orthogonally functional equation(1.3) through the classification of the oddness and evenness of f within the same spaces…”