Stability of the equation of homomorphism and completeness of the underlying space

• Autorzy: Moszner Z.
• Języki publikacji: EN

Abstrakty

EN

We prove that all assumptions of a Theorem of Forti and Schwaiger (cf. [4]) on the coherence of stability of the equation of homomorphism with the completeness of the space of values of all these homomorphisms, are essential. We give some generalizations of this theorem and certain examples of applications.

Słowa kluczowe

EN

functional equation; stability of equations of homomorphisms; superstability; complete vector spaces

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2008
• Tom: Vol. 28, no. 1
• Strony: 83--92
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Moszner Z.

• Pedagogical University of Cracow, Institute of Mathematics, Podchorążych 2, 30-084 Cracow, Poland,

Bibliografia

• [1] J.A. Baker, J. Lawrence, F. Zorzitto, The stability of the equation f(x + y) = f(x)f(y), Proc. Amer. Math. Soc. 74 (1979), 242–246.
• [2] G.L. Forti, The stability of homomorphisms and amenability,with applications to functional equations, Abh. Math. Sem. Univ. Hamburg 57 (1987), 215–226.
• [3] G.L. Forti, Hyers-Ulam stability of functional equations in several variables, Aequationes Math. 50 (1995), 143–190.
• [4] G.L. Forti, J. Schwaiger, Stability of homomorphisms and completeness, C. R. Math. Rep. Acad. Sci. Canada 11 (1989), 215–220.
• [5] D.H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. USA 27 (1941), 222–224.
• [6] D.H. Hyers, T.M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992), 125–153.
• [7] Z. Moszner, Sur la stabilite de l’equation d’homomorphisme, Aequationes Math. 29 (1985), 290–306.
• [8] Z. Moszner, On the stability of functional equations, Aequationes Math. (to appear).