Note on the stability of the system of functional equations

• Autorzy: Adam M.
• Języki publikacji: EN

Abstrakty

EN

We deal with the system of functional equations connected with additive and quadratic mappings. We correct some mistakes made in the paper [W. Fechner, On the Hyers-Ulam stability of functional equations connected with additive and quadratic mappings, J. Math. Anal. Appl. 322 (2006), 774–786] and provide accurate statements of those results. Moreover, we get the improvement of the Hyers-Ulam stability result of the considered system of functional equations.

Słowa kluczowe

EN

Hyers-Ulam-Rassias stability; additivity; quadratic functional equation

PL

stabilność Hyersa-Ulama-Rassiasa; addytywność; równanie funkcjonałów kwadratowych

• Wydawca: Wydawnictwo Politechniki Śląskiej
• Czasopismo: Silesian Journal of Pure and Applied Mathematics
• Rocznik: 2017
• Tom: Vol. 7, iss. 1
• Strony: 93--98
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Adam M.

• Institute of Mathematics, Silesian University of Technology, Gliwice, Poland

Bibliografia

• 1. Aczél J., Dhombres J.: Functional Equations in Several Variables. Encyclopedia Math. Appl., vol. 31. Cambridge Univ. Press, Cambridge 1989.
• 2. Drygas H.: Quasi-inner products and their applications. In: Advances in Multivariate Statistical Analysis, Theory and Decision Library (Series B: Mathematical and Statistical Methods), vol. 5, Gupta A.K. (ed.). Springer, Dordrecht 1987, 13–30.
• 3. Ebanks B.R., Kannappan Pl., Sahoo P.K.: A common generalization of functional equations characterizing normed and quasi-inner-product spaces. Canad. Math. Bull. 35 (1992), 321–327.
• 4. Fechner W.: On the Hyers-Ulam stability of functional equations connected with additive and quadratic mappings. J. Math. Anal. Appl. 322 (2006), 774–786.
• 5. Sikorska J.: On a direct method for proving the Hyers-Ulam stability of functional equations. J. Math. Anal. Appl. 372 (2010), 99–109.