On a Functional Which is Quadratic on A-orthogonal Vectors
Hamid Drljević (1986)
Publications de l'Institut Mathématique
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Hamid Drljević (1986)
Publications de l'Institut Mathématique
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Włodzimierz Fechner, Justyna Sikorska (2010)
Bulletin of the Polish Academy of Sciences. Mathematics
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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.
J. A. Lester (1976)
Colloquium Mathematicae
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Erwin Turdza (1970)
Annales Polonici Mathematici
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Youssef Aribou, Hajira Dimou, Abdellatif Chahbi, Samir Kabbaj (2015)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
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In this paper we prove the Hyers-Ulam stability of the following K-quadratic functional equation [...] where E is a real (or complex) vector space. This result was used to demonstrate the Hyers-Ulam stability on a set of Lebesgue measure zero for the same functional equation.
Bonnans, J.Frédéric, Ioffe, Alexander D. (1995)
Journal of Convex Analysis
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Jung, Soon-Mo (2000)
International Journal of Mathematics and Mathematical Sciences
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Gordji, M.Eshaghi (2009)
The Journal of Nonlinear Sciences and its Applications
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John Michael Rassias (2004)
Archivum Mathematicum
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In 1940 S. M. Ulam (Intersci. Publ., Inc., New York 1960) imposed at the University of Wisconsin the problem: “Give conditions in order for a linear mapping near an approximately linear mapping to exist”. According to P. M. Gruber (Trans. Amer. Math. Soc. 245 (1978), 263–277) the afore-mentioned problem of S. M. Ulam belongs to the following general problem or Ulam type problem: “Suppose a mathematical object satisfies a certain property approximately. Is it then possible to approximate...