Abstract
In this paper, we study the general solution of the functional equation, which is derived from additive–quartic mappings. In addition, we establish the generalized Hyers–Ulam stability of the additive–quartic functional equation in Banach spaces by using direct and fixed point methods.
Highlights
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The concept of stability for various functional equations arises when one replaces a functional equation by an inequality, which acts as a perturbation of the equation
Based on the above investigations, the main purpose of this paper is to prove the general solution of the additive–quartic functional equation of the form h(ηw1 + η 2 w2 + η 3 w3 ) + h(−ηw1 + η 2 w2 + η 3 w3 ) + h(ηw1 − η 2 w2 + η 3 w3 ) + h(ηw1 + η 2 w2 − η 3 w3 )
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The concept of stability for various functional equations arises when one replaces a functional equation by an inequality, which acts as a perturbation of the equation. The first stability problem of the functional equation was introduced by the mathematician S.M. Ulam [1] in 1940. Ulam [1] in 1940 Since this question has attracted the attention of many researchers
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