Browse > Article
http://dx.doi.org/10.4134/CKMS.c150249

LIPSCHITZ CRITERIA FOR BI-QUADRATIC FUNCTIONAL EQUATIONS  

Nikoufar, Ismail (Department of Mathematics Payame Noor University)
Publication Information
Communications of the Korean Mathematical Society / v.31, no.4, 2016 , pp. 819-825 More about this Journal
Abstract
In this paper, we establish approximation of bi-quadratic functional equations in Lipschitz spaces.
Keywords
bi-quadratic functional equation; Lipschitz space; stability;
Citations & Related Records
연도 인용수 순위
  • Reference
1 I. Nikoufar, Quartic functional equations in Lipschitz spaces, Rend. Circ. Mat. Palermo 64 (2015), no. 2, 171-176.   DOI
2 C. Park, On the stability of the quadratic mapping in Banach modules, J. Math. Anal. Appl. 276 (2002), no. 1, 135-144.   DOI
3 W.-G. Park and J.-H. Bae, Approximate behavior of bi-quadratic mappings in quasinormed spaces, J. Inequal. Appl. 2010 (2010), Art. ID 472721, 8 pages.
4 J. M. Rassias, Solution of the Ulam stability problem for quartic mappings, Glas. Mat. Ser. 34 (1999), no. 2, 243-252.
5 D. Sherbert, Banach algebras of Lipschitz functions, Pacific J. Math. 13 (1963), 1387-1399.   DOI
6 D. Sherbert, The structure of ideals and point derivations in Banach algebras of Lipschitz functions, Trans. Amer. Math. Soc. 111 (1964), 240-272.   DOI
7 F. Skof, Local properties and approximations of operators, Rend. Sem. Mat. Fis. Milano 53 (1983), 113-129.   DOI
8 J. Tabor, Lipschitz stability of the Cauchy and Jensen equations, Results Math. 32 (1997), no. 1-2, 133-144.   DOI
9 J. Tabor, Superstability of the Cauchy, Jensen and isometry equations, Results Math. 35 (1999), no. 3-4, 355-379.   DOI
10 P. W. Cholewa, Remarks on the stability of functional equations, Aequationes Math. 27 (1984), no. 1-2, 76-86.   DOI
11 S. Czerwik and K. Dlutek, Stability of the quadratic functional equation in Lipschitz spaces, J. Math. Anal. Appl. 293 (2004), no. 1, 79-88.   DOI
12 A. Ebadian, N. Ghobadipour, I. Nikoufar, and M. Gordji, Approximation of the cubic functional equations in Lipschitz spaces, Anal. Theory Appl. 30 (2014), no. 4, 354-362.
13 J. A. Johnson, Banach spaces of Lipschitz functions and vector-valued Lipschitz functions, Trans. Amer. Math. Soc. 148 (1970), 147-169.   DOI
14 S.-M. Jung and P. K. Sahoo, Hyers-Ulam stability of the quadratic equation of Pexider type, J. Korean Math. Soc. 38 (2001), no. 3, 645-656.
15 J. R. Lee, S.-Y. Jang, C. Park, and D. Y. Shin, Fuzzy stability of quadratic functional equations, Adv. Difference Equ. 2010 (2010), 16 pages, Article ID 412160.
16 I. Nikoufar, Perturbation of some functional equations in Lipschitz spaces, 44th Annual Iranian Mathematics Conference, Mashhad, 2013, Iran.