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2008 Functional Inequalities Associated with Additive Mappings
Jaiok Roh, Ick-Soon Chang
Abstr. Appl. Anal. 2008: 1-11 (2008). DOI: 10.1155/2008/136592

Abstract

The functional inequality f ( x ) + 2 f ( y ) + 2 f ( z ) 2 f ( 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 : G 3 [ 0 , ) are mappings, and X is a Banach space. The main result of the paper states that the assumptions above together with (1) ϕ ( 2 x , x , 0 ) = 0 = ϕ ( 0 , x , x ) ( x G ) and (2) lim n ( 1 / 2 n ) ϕ ( 2 n + 1 x , 2 n y , 2 n z ) = 0 , or lim n 2 n ϕ ( x / 2 n 1 , y / 2 n , z / 2 n ) = 0 ( x , y , z G ) , imply that f is additive. In addition, some stability theorems are proved.

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Jaiok Roh. Ick-Soon Chang. "Functional Inequalities Associated with Additive Mappings." Abstr. Appl. Anal. 2008 1 - 11, 2008. https://doi.org/10.1155/2008/136592

Information

Published: 2008
First available in Project Euclid: 10 February 2009

zbMATH: 1161.26012
MathSciNet: MR2438261
Digital Object Identifier: 10.1155/2008/136592

Rights: Copyright © 2008 Hindawi

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