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Stability of Dhombres' equation

Published online by Cambridge University Press:  17 April 2009

Bogdan Batko
Bogdan Batko
Affiliation:
Department of Mathematics, WSB - NLU, Zielona 27, 33–300 Nowy Sacz, Poland, e-mail: [email protected], Institute of Mathematics, Pedagogical University, Poduchorazych 2, 30–084 Kraków, Poland, e-mail: [email protected]
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One of the most important examples of conditional Cauchy equations with the condition dependent on the unknown function is Dhombres' equation This paper is devoted to the stability of the above equation.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 70 , Issue 3 , December 2004 , pp. 499 - 505
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Batko, B., ‘On the stability of Mikusiński's equation’ Publ. Math. Debrecen (to appear).Google Scholar
[2]Dhombres, J.G., Some aspects of functional equations (Chulalongkorn University, Bangkok, 1979).Google Scholar
[3]Dhombres, J.G. and Ger, R., ‘Conditional Caucky equations’, Glas. Mat. Ser. III 13 (1978), 39–62.Google Scholar
[4]Hyers, D.H., ‘On the stability of the linear functional equation’, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222–224.CrossRefGoogle ScholarPubMed
[5]Hyers, D.H., Isac, G. and Rassias, Th.M., ‘Stability of functional equations in several variables’ (Birkhäuser, Boston, Basel, Berlin).CrossRefGoogle Scholar
[6]Rätz, J., ‘On approximately additive mappings’, in General Inequalities 2 (Oberwolfach 1978) (Birkhäuser, Basel, Boston, 1980), pp. 233–251.CrossRefGoogle Scholar
[7]Schwaiger, J., ‘Report of Meeting, The 41st International Symposium of Functional Equations, Remark 13’, Aequationes Math. 67 (2004), 285–320.Google Scholar
[8]Ulam, S.M., A collection of mathematical problems (Interscience publ., New York, 1960).Google Scholar