Functional Inequalities Associated with Additive Mappings

Jaiok Roh and Ick-Soon Chang

Abstract and Applied Analysis, 2008, vol. 2008, issue 1

Abstract: 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.

Date: 2008
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2008/136592

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2008:y:2008:i:1:n:136592

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().