Fixed Point Approach: Ulam Stability Results of Functional Equation in Non-Archimedean Fuzzy φ-2-Normed Spaces and Non-Archimedean Banach Spaces

Abstract

In this work, we introduce a new type of generalized mixed-type quadratic-additive functional equation and obtain its general solution. The main goal of this work is to investigate Ulam stability of this mixed type of quadratic-additive functional equation in the setting of non-Archimedean fuzzy φ-2-normed space and non-Archimedean Banach space using the direct and fixed point approaches by taking into our account two cases: even mapping and odd mapping.

Fuzzy stability of functional equations via fixed point theorem

“…In particular, the Banach fixed point theorem has been used extensively to prove stability results for various functional equations, such as the Cauchy functional equation, the Jensen functional equation, and the quadratic functional equation. One of the most important applications of fixed point theory in Hyers-Ulam stability is the proof of the Hyers-Ulam-Rassias stability theorem (see for instance [19,20,21]). The fixed point theorem provides a powerful tool for studying the stability of functional equations in non-smooth settings.…”

Generalized Hyers-Ulam stability of a bi-quadratic mapping in non-Archimedean spaces

“…Very recently, Tamilvanan et al [42] introduced a new type of generalized mixed-type quadraticadditive functional equation and obtained its general solution and investigated the Ulam stability of the mixed type of quadratic-additive functional equation in non-Archimedean fuzzy φ-2-normed space and non-Archimedean Banach space using the direct and fixed point approaches by taking into even and odd mapping.…”

Fixed point approach to the stability of a cubic and quartic mixed type functional equation in non-archimedean spaces

“…then f, g and h may be approximated by A 1 mapping in NA normed spaces. Very recently, Tamilvanan et al [29] created a new type of generalized mixed-type A 1 Q 2 FE and obtained its general solution and proved the Ulam stability of the mixed type A 1 Q 2 FE in NA fuzzy ϕ-2normed space and NA Banach space using the direct and fixed point approaches by taking into even and odd mapping. The HUR stability for a mixed type C 3 Q 4 FE (1.3) for any υ, ν ∈ A, in NA Banach spaces will be established in this article using the fixed point approach.…”