On the superstability of the generalized orthogonality equation in Euclidean spaces
Abstract
We consider a class of approximate solutions of the generalized orthogonality equation in ℝn (n≥2). We prove that this class coincides with the class of solutions of the equation, i.e., the superstability of the generalized orthogonality equation holds.
References
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2. C. Alsina, J.L. Garcia-Roig, On the functional equation |T(x)◦T(y)| = |x◦y|, Constantin Carathéodory: An International Tribute, ed. by Th.M. Rassias, World Scientific Publ. Co. 1991, 47-52.
3. J. Chmieliński, On the Hyers-Ulam stability of the generalized orthogonality equation in real Hilbert spaces, to appear.
4. J. Chmieliński, On the stability of the generalized orthogonality equation, to appear.
5. R. Ger, Superstability is not natural, Rocznik Naukowo - Dydaktyczny WSP w Krakowie, Prace Matematyczne XIII (Annales de l'Ecole Normale Supérieure à Cracovie, Travaux Mathématiques XIII), Kraków 1993, 109-123.
6. D.H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222-224.
7. J.S. Lomont, P. Mendelson, The Wigner unitarity-antiunitarity theorem, Ann. of Math. 78 (1963), 548-559.
8. J. Rätz, Remarks on Wigner's Theorem, talk given during 31-st International Symposium on Functional Equations, Debrecen, Hungary 1993.
9. E.P. Wigner, Gruppentheorie und ihre Anwendungen auf die Quantenmechanik der Atomspektren, Friedr. Vieweg und Sohn Akt.-Ges., 1931, 251.
ChmielińskiJ. (1994). On the superstability of the generalized orthogonality equation in Euclidean spaces. Annales Mathematicae Silesianae, 8, 127-140. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14224
Jacek Chmieliński
Instytut Matematyki, Wyższa Szkoła Pedagogiczna im. Komisji Edukacji Narodowej w Krakowie Poland
Instytut Matematyki, Wyższa Szkoła Pedagogiczna im. Komisji Edukacji Narodowej w Krakowie Poland
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