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On the Stability of a Higher Functional Equation in Banach Algebras

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경북대학교 자연과학대학 수학과|2019.12|Kyungpook Mathematical Journal|제59권 제4호|pp. 689-701|DOI 10.5666/KMJ.2019.59.4.689

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stabilityhigher functional equation
주제분류수학

초록

Let A and B be real (or complex) algebras. We investigate the stability of a sequence F = {f, f_0, f_1, ... , f_n, ... } of mappings from A into B satisfying the higher functional equation:f_n(x + y + zw) = f_n(x) + f_n(y) +Σ_{i+j=n, i<=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} =1 if i ≠ j; 0 if i = j

Abstract

Let A and B be real (or complex) algebras. We investigate the stability of a sequence F = {f, f_0, f_1, ... , f_n, ... } of mappings from A into B satisfying the higher functional equation:f_n(x + y + zw) = f_n(x) + f_n(y) +Σ_{i+j=n, i<=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} =1 if i ≠ j; 0 if i = j

참고문헌 (18)

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