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http://dx.doi.org/10.5666/KMJ.2019.59.4.689

On the Stability of a Higher Functional Equation in Banach Algebras  

Jung, Yong-Soo (Department of Mathematics, Sun Moon University,)
Publication Information
Kyungpook Mathematical Journal / v.59, no.4, 2019 , pp. 689-702 More about this Journal
Abstract
Let 𝓐 and 𝓑 be real (or complex) algebras. We investigate the stability of a sequence F = {f0, f1, ⋯, fn, ⋯ } of mappings from 𝓐 into 𝓑 satisfying the higher functional equation: $$f_n(x+y+zw)=f_n(x)+f_n(y)+\;{\normalsize\sum\limits_{\tiny{i+j=n \atop i{\leq}j}}}\;[f_i(z)f_j(w)+c_{ij}f_i(w)f_j(z)]$$ for each n = 0, 1, ⋯ and all x, y, z, w ∈ 𝓐, where $$c_{ij}=\left\{1{\text{ if }}i{\neq}j,\\0{\text{ if }}i=j.\right.$$.
Keywords
higher functional equation; stability;
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