Stability of an Additive‐Cubic‐Quartic Functional Equation in Multi‐Banach Spaces

Abstract

We prove the Hyers-Ulam stability of the additive-cubic-quartic functional equation in multi-Banach spaces by using the fixed point alternative method. The first results on the stability in the multi-Banach spaces were presented in (Dales and Moslehian 2007).

Stability of Functional Equations in Multi-Banach Spaces via Fixed Point Approach

“…The asymptotic aspects of the quadratic functional equations in multi-normed spaces was investigated by M. S. Moslehian, K. Nikodem, and D. Popa [9] in 2009. In last two decades, the stability of functional equations on multi-normed spaces was proved by many mathematicians ( [7], [10], [21]). Now, we adopt some usual terminology, notion and convention of the theory of multi-Banach spaces from [4] and [5].…”

Stability of Orthogonally Additive-Quadratic Functional Equation in Multi-Banach Spaces

“…In 2011, Zhihua Wang, Xiaopei Li and Th. M. Rassias [21] proved the Hyers -Ulam stability of the additive -cubic -quartic functional equations…”

Stability of an ACQ-functional equation in various matrix normed spaces

“…In [6], the authors established the general solution and proved the generalized Hyers-Ulam stability of the functional equation (1.1) in Banach spaces. And using the fixed point method, the Hyers-Ulam stability results for the functional equation (1.1) in fuzzy Banach spaces and multi-Banach spaces were established in [12,27], respectively. The main purpose of this paper is to apply the direct method and fixed point method to investigate the Hyers-Ulam stability of functional equation (1.1) in matrix Banach spaces.…”