A FIXED POINT APPROACH TO THE STABILITY OF A GENERAL MIXED ADDITIVE-CUBIC EQUATION ON BANACH MODULES
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.
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| Published in: | Acta mathematica scientia Vol. 32; no. 3; pp. 866 - 892 |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier Ltd
01-05-2012
Department of Electrical and Computer Engineering, College of Engineering, University of Kentucky,Lexington 40506, USA School of Mathematics, Beijing Institute of Technology, Beijing 100081, China%Pedagogical Department E.E., Section of Mathematics and Informatics, National and Capodistrian University of Athens, 4, Agamemnonos Str., Aghia Paraskevi, Athens 15342, Greece%School of Communication and Information Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China |
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| Online Access: | Get full text |
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| Summary: | 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. |
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| Bibliography: | 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 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. 42-1227/O ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| ISSN: | 0252-9602 1572-9087 |
| DOI: | 10.1016/S0252-9602(12)60067-8 |