Stability of the equation of ring homomorphisms

• Autorzy: Ger R.
• Języki publikacji: EN

Abstrakty

EN

Let R be a unitary ring and (A,║‧║) stand for a Banach algebra with a unit. In connection with some stability results of R. Badora [1] and D.G. Bourgin [2] concerning the system of two Cauchy functional equations [formula] for mappings f : R→ A, we deal with Hyers-Ulam stability problem for a single equation f(x + y) + f(xy) = f(x) + f(y) + f(x)f(y). The basic question whether or not equation (**) is equivalent to the system (*) has widely been examined by J. Dhombres [3] and the present author in [4] and [5].

Słowa kluczowe

EN

algebra; Banach algebra; homomorphism

PL

algebra; algebra Banacha; homomorfizm algebr

• Wydawca: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie
• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 2007
• Tom: Vol. 12
• Strony: 29--35
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Ger R.

• Institute of Mathematics and Computer Science Jan Długosz University of Częstochowa al. Armii Krajowej 19/15, 42-200 Częstochowa, Poland

Bibliografia

• [1] R. Badora. On approximate ring homomorphisms. J. Math, Anal. Appl., 276, 589-597, 2002.
• [2] D.G. Bourgin. Approximately isometric and multiplicative transformations on continuous function rings. Duke Math. J., 16, 385-397, 1949.
• [3] J. Dhombres. Relations de dépendance entre les equations fonctionnelles de Cauchy. Aequationes Math., 3;5, 186-212, 1988.
• [4] R. Ger. On an equation of ring homomorphisms. Publ. Math. Debrecen, 52, 397-417, 1998.
• [5] R. Ger. Ring homomorphisms equation revisited. Rocznik Nauk.-Dydakt. Prace Mat., 17, 101-115, 2000.
• [6] D. H. Hyers. On the stability of the linear functional equation. Proc. Nat. Acad. Sci. U.S.A., 21, 222-224, 1941.