On the stability of orthogonal additivity

• Autorzy: Fechner W. , Sikorska J.
• Języki publikacji: EN

Abstrakty

EN

We deal with the stability of the orthogonal additivity equation, presenting a new approach to the proof of a 1995 result of R, Ger and the second author. We sharpen the estimate obtained there. Moreover, we work in more general settings, providing an axiomatic framework which covers much more cases than considered before by other authors.

Słowa kluczowe

EN

orthogonal additivity; stability

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2010
• Tom: Vol. 58, no 1
• Strony: 23--30
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Fechner W.

autor

Sikorska J.

• Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland,

Bibliografia

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• [3] W. Fechner, On the Hyers-Ulam stability of functional equations connected with additive and quadratic mappings, J. Math. Anal. Appl. 322 (2006), 774-786.
• [4] R. Ger and J. Sikorska, Stability of the orthogonal additivity, Bull. Polish Acad. Sci. Math. 43 (1995), 143-151.
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• [11] J. Rätz, On orthogonally additive mappings, ibid. 28 (1985), 35-49.
• [12] J. Rätz, On orthogonally additive mappings. II, Publ. Math. Debrecen 35 (1988), 241-249.
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• [15] J. Sikorska, Orthogonal stability of some functional equations, PhD Thesis, Silesian Univ., Katowice, 1997 (in Polish).
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• [17] Gy. Szabó, A conditional Cauchy equation on normed spaces, Publ. Math. Debrecen 42 (1993), 256-271.
• [18] Gy. Szabó, Isosceles orthogonally additive mappings and inner product spaces, ibid. 46 (1995), 373-384.