Functional equations motivated by the Lagrange's identity

• Autorzy: Fechner W.
• Języki publikacji: EN

Abstrakty

EN

(...)

Słowa kluczowe

EN

Lagrange's identity; quadratic mappings; multiplicative mappings; additive-multiplicative functionals; Euler-Lagrange quadratic mappings; Euler-Lagrange functional equation

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2011
• Tom: Vol. 44, nr 1
• Strony: 91--98
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Fechner W.

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

Bibliografia

• [1] J. Aczél, J. Dhombres, Functional equations in several variables, Encyclopedia Math. Appl. 31, Cambridge Univ. Press, Cambridge, 1989.
• [2] K. Baron, P. Volkmann, On orthogonally additive functions, Publ. Math. Debrecen 52 (1998), 291–297.
• [3] Z. Gajda, On multiplicative solutions of the parallelogram function al equation, Abh. Math. Sem. Univ. Hamburg 63 (1993), 59–66.
• [4] C. Hammer, P. Volkmann, Die multiplikativen Lösungen der Parallelogrammgleichung, Abh. Math. Sem. Univ. Hamburg 61 (1991), 197–201.
• [5] H.-M. Kim, J. M. Rassias, Y.-S. Cho, Stability problem of Ulam for Euler–Lagrange quadratic mappings, J. Inequal. Appl. 2007, Art. ID 10725, 15 pp.
• [6] H.-M. Kim, J. M. Rassias, Generalization of Ulam stability problem for Euler–Lagrange quadratic mappings, J. Math. Anal. Appl. 336 (2007), 277–296.
• [7] M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities (second edition), Birkhäuser, Basel, Boston, Berlin, 2009.
• [8] A. Pietrzyk, Stability of the Euler–Lagrange–Rassias functional equation, Demonstratio Math. 39 (2006), 523–530.
• [9] J. M. Rassias, On the stability of the general Euler–Lagrange functional equation, Demonstratio Math. 29 (1996), 755–766.
• [10] J. M. Rassias, Solution of the Ulam stability problem for Euler–Lagrange quadratic mappings, J. Math. Anal. Appl. 220 (1998), 613–639.
• [11] J. M. Rassias, On the Hyers-Ulam stability problem for quadratic multi-dimensional mappings, Aequationes Math. 64 (2002), 62–69.
• [12] J. M. Rassias, On the stability of the multi-dimensional Euler–Lagrange functional equation, J. Indian Math. Soc. (N. S.) 66 (1999), 1–9.
• [13] M. J. Rassias, J. M. Rassias, On the Ulam stability for Euler–Lagrange type quadratic functional equations, Aust. J. Math. Anal. Appl. 2 (2005), no. 1, Art. 11, 10 pp. (electronic).