Characterization and Stability of Multimixed Additive-Quartic Mappings: A Fixed Point Application

Abstract

In this article, we introduce the multi-additive-quartic and the multimixed additive-quartic mappings. We also describe and characterize the structure of such mappings. In other words, we unify the system of functional equations defining a multi-additive-quartic or a multimixed additive-quartic mapping to a single equation. We also show that under what conditions, a multimixed additive-quartic mapping can be multiadditive, multiquartic, and multi-additive-quartic. Moreover, by using a fixed point technique, we prove the Hyers-Ulam stability of multimixed additive-quartic functional equations thus generalizing some known results.

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.…”

Orthogonally C∗‐Ternary Jordan Homomorphisms and Jordan Derivations: Solution and Stability

“…In 1987, Rassias [3] proved a generalized version of the Hyers' theorem for approximately additive maps. Te study of stability problem of functional equations have been done by several authors on diferent spaces such as Banach, C * -Banach algebras and modular spaces (for example see [4][5][6][7][8][9][10][11][12][13]). One of the stimulating aspects is to examine the stability of those functional equations whose general solutions exist and are useful in characterizing entropies [14].…”