A FIXED POINT APPROACH TO THE STABILITY OF A GENERAL MIXED ADDITIVE-CUBIC EQUATION ON BANACH MODULES

doi:10.1016/S0252-9602(12)60067-8

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (3): 866-892.doi: 10.1016/S0252-9602(12)60067-8

A FIXED POINT APPROACH TO THE STABILITY OF A GENERAL MIXED ADDITIVE-CUBIC EQUATION ON BANACH MODULES

许天周^1*|Rassias John Michael²|许婉欣³

1.School of Mathematics, Beijing Institute of Technology, Beijing 100081, China|2.Pedagogical Department E.E., Section of Mathematics and Informatics, National and Capodistrian University of Athens, 4, gamemnonos Str., Aghia Paraskevi, Athens 15342, Greece|3.School of Communication and Information Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China|Department of Electrical and Computer Engineering, College of Engineering, University of Kentucky, Lexington 40506, USA

收稿日期:2010-01-25 修回日期:2011-02-18 出版日期:2012-05-20 发布日期:2012-05-20
通讯作者: XU Tian-Zhou,xutianzhou@bit.edu.cn E-mail:xutianzhou@bit.edu.cn; jrassias@primedu.uoa.gr; wxbit0930@gmail.com
基金资助:
The first author was supported by the National Natural Science Foundation of China (10671013, 60972089, 11171022).

A FIXED POINT APPROACH TO THE STABILITY OF A GENERAL MIXED ADDITIVE-CUBIC EQUATION ON BANACH MODULES

XU Tian-Zhou^1*, Rassias John Michael², XU Wan-Xin³

1.School of Mathematics, Beijing Institute of Technology, Beijing 100081, China|2.Pedagogical Department E.E., Section of Mathematics and Informatics, National and Capodistrian University of Athens, 4, gamemnonos Str., Aghia Paraskevi, Athens 15342, Greece|3.School of Communication and Information Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China|Department of Electrical and Computer Engineering, College of Engineering, University of Kentucky, Lexington 40506, USA

Received:2010-01-25 Revised:2011-02-18 Online:2012-05-20 Published:2012-05-20
Contact: XU Tian-Zhou,xutianzhou@bit.edu.cn E-mail:xutianzhou@bit.edu.cn; jrassias@primedu.uoa.gr; wxbit0930@gmail.com
Supported by:
The first author was supported by the National Natural Science Foundation of China (10671013, 60972089, 11171022).

摘要/Abstract

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) − 2kf(x) in Banach modules over a unital Banach algebra.

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

Abstract:

Key words: 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

中图分类号:

39B72

许天周, Rassias John Michael, 许婉欣. A FIXED POINT APPROACH TO THE STABILITY OF A GENERAL MIXED ADDITIVE-CUBIC EQUATION ON BANACH MODULES[J]. 数学物理学报(英文版), 2012, 32(3): 866-892.

XU Tian-Zhou, Rassias John Michael, XU Wan-Xin. A FIXED POINT APPROACH TO THE STABILITY OF A GENERAL MIXED ADDITIVE-CUBIC EQUATION ON BANACH MODULES[J]. Acta mathematica scientia,Series B, 2012, 32(3): 866-892.

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A FIXED POINT APPROACH TO THE STABILITY OF A GENERAL MIXED ADDITIVE-CUBIC EQUATION ON BANACH MODULES

A FIXED POINT APPROACH TO THE STABILITY OF A GENERAL MIXED ADDITIVE-CUBIC EQUATION ON BANACH MODULES

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