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Functional Inequalities Associated with Additive Mappings
Joint Authors
Source
Issue
Vol. 2008, Issue 2008 (31 Dec. 2008), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2008-09-10
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
The functional inequality ‖f(x)+2f(y)+2f(z)‖≤‖2f(x/2+y+z)‖+ϕ (x,y,z) (x,y,z∈G) is investigated, where G is a group divisible by 2,f:G→X and ϕ:G3→[0,∞) are mappings, and X is a Banach space.
The main result of the paper states that the assumptions above together with (1) ϕ(2x,−x,0)=0=ϕ(0,x,−x) (x∈G) and (2) limn→∞(1/2n)ϕ(2n+1x,2ny,2nz)=0, or limn→∞2nϕ(x/2n−1,y/2n,z/2n)=0 (x,y,z∈G), imply that f is additive.
In addition, some stability theorems are proved.
American Psychological Association (APA)
Roh, Jaiok& Chang, Ick-Soon. 2008. Functional Inequalities Associated with Additive Mappings. Abstract and Applied Analysis،Vol. 2008, no. 2008, pp.1-11.
https://search.emarefa.net/detail/BIM-448585
Modern Language Association (MLA)
Roh, Jaiok& Chang, Ick-Soon. Functional Inequalities Associated with Additive Mappings. Abstract and Applied Analysis No. 2008 (2008), pp.1-11.
https://search.emarefa.net/detail/BIM-448585
American Medical Association (AMA)
Roh, Jaiok& Chang, Ick-Soon. Functional Inequalities Associated with Additive Mappings. Abstract and Applied Analysis. 2008. Vol. 2008, no. 2008, pp.1-11.
https://search.emarefa.net/detail/BIM-448585
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-448585