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

Faruk Polat

Abstract and Applied Analysis, 2012, vol. 2012, 1-9

Abstract:

Badora (2002) proved the following stability result. Let 𠜀 and ð ›¿ be nonnegative real numbers, then for every mapping ð ‘“ of a ring â„› onto a Banach algebra ℬ satisfying | | ð ‘“ ( ð ‘¥ + 𠑦 ) − ð ‘“ ( ð ‘¥ ) − ð ‘“ ( 𠑦 ) | | ≤ 𠜀 and | | ð ‘“ ( ð ‘¥ â‹… 𠑦 ) − ð ‘“ ( ð ‘¥ ) ð ‘“ ( 𠑦 ) | | ≤ ð ›¿ for all ð ‘¥ , 𠑦 ∈ â„› , there exists a unique ring homomorphism â„Ž ∶ â„› → ℬ such that | | ð ‘“ ( ð ‘¥ ) − â„Ž ( ð ‘¥ ) | | ≤ 𠜀 , ð ‘¥ ∈ â„› . Moreover, ð ‘ â‹… ( ð ‘“ ( ð ‘¥ ) − â„Ž ( ð ‘¥ ) ) = 0 , ( ð ‘“ ( ð ‘¥ ) − â„Ž ( ð ‘¥ ) ) â‹… ð ‘ = 0 , for all ð ‘¥ ∈ â„› and all ð ‘ from the algebra generated by â„Ž ( â„› ) . In this paper, we generalize Badora's stability result above on ring homomorphisms for Riesz algebras with extended norms.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:653508

DOI: 10.1155/2012/653508

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