Some Generalizations of Ulam‐Hyers Stability Functional Equations to Riesz Algebras

Faruk Polat

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: Badora (2002) proved the following stability result. Let ε and δ be nonnegative real numbers, then for every mapping f of a ring ℛ onto a Banach algebra ℬ satisfying | | f(x + y) − f(x) − f(y)|| ≤ ε and | | f(x · y) − f(x)f(y)|| ≤ δ for all x, y ∈ ℛ, there exists a unique ring homomorphism h : ℛ → ℬ such that | | f(x) − h(x)|| ≤ ε, x ∈ ℛ. Moreover, b · (f(x) − h(x)) = 0, (f(x) − h(x)) · b = 0, for all x ∈ ℛ and all b from the algebra generated by h(ℛ). In this paper, we generalize Badora′s stability result above on ring homomorphisms for Riesz algebras with extended norms.

Date: 2012
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2012/653508

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:2012:y:2012:i:1:n:653508

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 ().