A fixed point approach to the stability of a general mixed additive-cubic equation on banach modules

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• 作者：Xu Tianzhou^a ; ^{xutianzhou@bit.edu.cn} ; Rassias John Michael^b ; ^{jrassias@primedu.uoa.gr} ; Xu Wanxin^c ; ^d ; ^{wxbit0930@gmail.com}
• 关键词：Banach module ; stability ; additive function ; cubic function ; unital Banach ; algebra ; generalized metric space ; fixed-point ; JMRassias (or JMR) mixed product-sum of powers of norms
• 刊名：Acta Mathematica Scientia
• 出版年：2012
• 期刊代码：1_02529602
• 类别：mt
• 出版时间：May, 2012
• 卷：32
• 期：3
• 页码：866-892
• 文件大小：333 K

摘要

Using a fixed-point method, we establish the generalized Hyers-Ulam stability of a general mixed additive-cubic equation: f(kx+y) + f(kx-y) = kf(x+y) + kf(x-y) + 2f(kx) 鈭?2kf(x) in Banach modules over a unital Banach algebra.