Stability of the Euler-Lagrange-Rassias functional equation

• Autorzy: Pietrzyk A.
• Języki publikacji: EN

Abstrakty

EN

Let F be a field, a1, a2 is an element of F, K is an element of {R, C}, s an element of K\{0,1}, X be a linear space over F, S C is contained in X be nonempty, and Y be a Banach space over K. Under some additional assumptions on S we show some stability results for the functional equation Q (a1x + a2y) + Q (a2X - a1y) = s[Q{x) + Q{y)} in the class of function Q : S -> Y.

Słowa kluczowe

EN

functional equations; Euler-Lagrange equations; Banach space; normed space

PL

równania funkcyjne; równania Eulera-Lagrange'a; przestrzeń Banacha; przestrzeń unormowana

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 3
• Strony: 523--530
• Opis fizyczny: BIbliogr. 14 poz.

Twórcy

autor

Pietrzyk A.

• Institute Mathematics, Silesian University, ul. Bankowa 14, 40-007 Katowice, Poland,

Bibliografia

• [1] R. P. Agarwal, B. Xu,W. Zhang, Stability of functional equations in single variable, J. Math. Anal. Appl. 288 (2003), 852-869.
• [2] J. A. Baker, The stability of certain functional equations, Proc. Amer. Math. Soc. 112 (1991), 729-732.
• [3] P.W. Cholewa, Remarks on the stability of functional equations, Aequationes Math. 27 (1984), 78-86.
• [4] R. Ger, Stability of ?-additive mappings and Orlicz ?2 condition - presented at The Władysław Orlicz Centenary Conference and Function Spaces VII, Poznań, July 21-25, 2003.
• [5] R. Ger, Stability of ?-additive mappings and Orlicz ?2 condition. The Władysław Orlicz Centenary Conference and Function Spaces VII, Poznań, July 21-25, 2003 Abstracts, Faculty of Mathematics and Computer Science Adan Mickiewicz University, Poznań.
• [6] J. M. Rassias, On the stability of the Euler-Lagrange functional equation, Chinese J. Math. 20 (1992), no. 2, 185-190.
• [7] J. M. Rassias, On the stability of the Euler-Lagrange functional equation, C. R. Acad. Bulgare Sci. 45 (1992), no. 6, 17-20.
• [8] J.M. Rassias, On the stability of the non-linear Euler-Lagrange functional equation in real normed linear spaces, C. R. Acad. Bulgare Sci. 46 (1993), no. 9, 13-15 (1994).
• [9] J. M. Rassias, On the stability of the non-linear Euler-Lagrange functional equation in real normed linear spaces, J. Math. Phys. Sci. 28 (1994), no. 5, 231-235.
• [10] J. M. Rassias, On the stability of the general Euler-Lagrange functional equation, Demonstratio Math. 29 (1996), no. 4, 755-766.
• [11] J. M. Rassias, Solution of the Ulam stability problem for Euler-Lagrange quadratic mappings, J. Math. Anal. Appl. 220 (1998), no. 2, 613-639.
• [12] J. M. Rassias, On the stability of the multi-dimensional Euler-Lagrange functional equation, J. Indian Math. Soc. (N.S.) 66 (1999), no. 1-4, 1-9.
• [13] J. M. Rassias, On approximation of approximately quadratic mappings by quadratic mappings, Ann. Math. Sil. No. 15 (2001), 67-78.
• [14] J. M. Rassias, On the Ulam stability of mixed type mappings on restricted domains, J. Math. Anal. Appl. 276 (2002), no. 2, 747-762.