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

Faruk Polat | Zendy

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

Author(s) -

Faruk Polat

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/653508

Subject(s) - mathematics , stability (learning theory) , pure mathematics , riesz representation theorem , algebra over a field , mathematical analysis , computer science , machine learning

Badora (2002) proved the following stability result. Let and be nonnegative real numbers, then for every mapping of a ring ℛ onto a Banach algebra ℬ satisfying ||(+)−()−()||≤ and ||(⋅)−()()||≤ for all ,∈ℛ, there exists a unique ring homomorphism ℎ∶ℛ→ℬ such that ||()−ℎ()||≤,∈ℛ. Moreover, ⋅(()−ℎ())=0,(()−ℎ())⋅=0, for all ∈ℛ and all 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

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