On the superstability of certain function equations

• Autorzy: Trif T.
• Języki publikacji: EN

Abstrakty

EN

We prove new results concerning the superstability of the equation (2) (both in the conventional sense and in the sense of R. Ger) and of the equation (3) (in the conventional sense). Likewise, we provide new simple proofs for stronger versions of already known results on the superstability of the equation (1) (both in the conventional sense and in the sense of R. Ger) and of the equation (3) (in the sense of R. Ger).

Słowa kluczowe

EN

certain functional equations; homogeneity; homogeneous equations

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2002
• Tom: Vol. 35, nr 4
• Strony: 813--820
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Trif T.

• Universitatea Babeş-Bolyai, Facultatea de Matematică şi Informatică, Str. Kogălniceanu 1, 3400 Cluj-Napoca, Romania

Bibliografia

• [1] J. Chudziak, Stability of the homogeneous equation, Demonstratio Math. 31 (1998), 765-772.
• [2] S. Czerwik, On the stability of homogeneous mappings, C. R. Math. Rep. Acad. Sci. Canada 14 (1992), 268-272.
• [3] R. Ger, Superstability is not natural, Rocznik Naukowo-Dydaktyczny WSP w Krakowie, Prace Mat. 159 (1993), 109-123.
• [4] D. H. Hyers, G. Isac and Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Boston-Basel-Berlin, 1998.
• [5] S.-M. Jung, On the superstability of the functional equation f ( x y ) = y f ( x ) , Abh. Math. Sem. Univ. Hamburg 67 (1997), 315-322.
• [6] S.-M. Jung, On a modified Hyers-Ulam stability of homogeneous equation, Int. J. Math. Math. Sci. 21 (1998), 475-478.
• [7] S.-M. Jung, Superstability of homogeneous functional equation, Kyungpook Math. J. 38 (1998), 251-257.
• [8] J. Milkman, Note on the functional equations f(xy) - f ( x ) + f ( y ) , f ( x n ) = nf(x), Proc. Amer. Math. Soc. 1 (1950), 505-508.
• [9] J. Tabor and J. Tabor, Homogeneity is superstable, Publ. Math. Debrecen 45 (1994), 123-130.