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A FIXED POINT APPROACH TO THE CAUCHY-RASSIAS STABILITY OF GENERAL JENSEN TYPE QUADRATIC-QUADRATIC MAPPINGS
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 Title & Authors
A FIXED POINT APPROACH TO THE CAUCHY-RASSIAS STABILITY OF GENERAL JENSEN TYPE QUADRATIC-QUADRATIC MAPPINGS
Park, Choon-Kil; Gordji, M. Eshaghi; Khodaei, H.;
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 Abstract
In this paper, we investigate the Cauchy-Rassias stability in Banach spaces and also the Cauchy-Rassias stability using the alternative fixed point for the functional equation: $$f(\frac{sx+ty}{2}+rz)+f(\frac{sx+ty}{2}-rz)+f(\frac{sx-ty}{2}+rz)+f(\frac{sx-ty}{2}-rz)
 Keywords
Cauchy-Rassias stability;quadratic mapping;fixed point method;
 Language
English
 Cited by
1.
Approximate homomorphisms and derivations on random Banach algebras, Journal of Inequalities and Applications, 2012, 2012, 1, 157  crossref(new windwow)
2.
On the Stability of an -Variables Functional Equation in Random Normed Spaces via Fixed Point Method, Discrete Dynamics in Nature and Society, 2012, 2012, 1  crossref(new windwow)
 References
1.
J. Aczel and J. Dhombres, Functional Equations in Several Variables, Cambridge University Press, Cambridge, 1989.

2.
J. Bae and W. Park, Generalized Jensen’s functional equations and approximate algebra homomorphisms, Bull. Korean Math. Soc. 39 (2002), no. 3, 401-410. crossref(new window)

3.
D. Boo, S. Oh, C. Park, and J. Park, Generalized Jensen’s equations in Banach modules over a $C^*$-algebra and its unitary group, Taiwanese J. Math. 7 (2003), no. 4, 641-655. crossref(new window)

4.
L. Cadariu and V. Radu, On the stability of the Cauchy functional equation: a fixed point approach, Iteration theory (ECIT ’02), 43-52, Grazer Math. Ber., 346, Karl-Franzens-Univ. Graz, Graz, 2004.

5.
L. Cadariu and V. Radu, The fixed points method for the stability of some functional equations, Carpathian J. Math. 23 (2007), no. 1-2, 63-72.

6.
L. Cadariu and V. Radu, Fixed points and the stability of quadratic functional equations, An. Univ. Timisoara Ser. Mat.-Inform. 41 (2003), no. 1, 25-48.

7.
St. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg 62 (1992), 59-64. crossref(new window)

8.
J. B. Diaz and B. Margolis, A fixed point theorem of the alternative, for contractions on a generalized complete metric space, Bull. Amer. Math. Soc. 74 (1968), 305-309. crossref(new window)

9.
Z. Gajda, On stability of additive mappings, Internat. J. Math. Math. Sci. 14 (1991), no. 3, 431-434. crossref(new window)

10.
D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. U.S.A. 27 (1941), 222-224. crossref(new window)

11.
S. Jung, Hyers-Ulam-Rassias stability of Jensen's equation and its application, Proc. Amer. Math. Soc. 126 (1998), no. 11, 3137-3143. crossref(new window)

12.
Y. Jung and I. Chang, The stability of a cubic type functional equation with the fixed point alternative, J. Math. Anal. Appl. 306 (2005), no. 2, 752-760. crossref(new window)

13.
Pl. Kannappan, Quadratic functional equation and inner product spaces, Results Math. 27 (1995), no. 3-4, 368-372. crossref(new window)

14.
Y. Lee and K. Jun, A generalization of the Hyers-Ulam-Rassias stability of Jensen's equation, J. Math. Anal. Appl. 238 (1999), no. 1, 305-315. crossref(new window)

15.
M. Mirzavaziri and M. S. Moslehian, A fixed point approach to stability of a quadratic equation, Bull. Braz. Math. Soc. (N.S.) 37 (2006), no. 3, 361-376. crossref(new window)

16.
M. S. Moslehian and L. Szekelyhidi, Stability of ternary homomorphisms via generalized Jensen equation, Results Math. 49 (2006), no. 3-4, 289-300. crossref(new window)

17.
C. Park, Modified Trifs functional equations in Banach modules over a $C^{\ast}$-algebra and approximate algebra homomorphisms, J. Math. Anal. Appl. 278 (2003), no. 1, 93-108. crossref(new window)

18.
C. Park, Generalized quadratic mappings in several variables, Nonlinear Anal. 57 (2004), no. 5-6, 713-722. crossref(new window)

19.
C. Park, S. Hong, and M. Kim, Jensen type quadratic-quadratic mapping in Banach spaces, Bull. Korean Math. Soc. 43 (2006), no. 4, 703-709. crossref(new window)

20.
C. Park, J. Park, and J. Shin, Hyers-Ulam-Rassias stability of quadratic functional equations in Banach modules over a $C^*$-algebra, Chinese Ann. Math. Ser. B 24 (2003), no. 2, 261-266. crossref(new window)

21.
V. Radu, The fixed point alternative and the stability of functional equations, Fixed Point Theory 4 (2003), no. 1, 91-96.

22.
J. M. Rassias and M. J. Rassias, Asymptotic behavior of Jensen and Jensen type functional equations, Panamer. Math. J. 15 (2005), no. 4, 21-35.

23.
J. M. Rassias and M. J. Rassias, Asymptotic behavior of alternative Jensen and Jensen type functional equations, Bull. Sci. Math. 129 (2005), no. 7, 545-558. crossref(new window)

24.
Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300. crossref(new window)

25.
Th. M. Rassias and P. Semrl, On the behavior of mappings which do not satisfy Hyers-Ulam stability, Proc. Amer. Math. Soc. 114 (1992), no. 4, 989-993. crossref(new window)

26.
Th. M. Rassias and K. Shibata, Variational problem of some quadratic functionals in complex analysis, J. Math. Anal. Appl. 228 (1998), 234-253. crossref(new window)

27.
F. Skof, Local properties and approximation of operators, Rend. Sem. Mat. Fis. Milano 53 (1983), 113-129. crossref(new window)

28.
T. Trif, On the stability of a functional equation deriving from an inequality of Popoviciu for convex functions, J. Math. Anal. Appl. 272 (2002), no. 2, 604-616. crossref(new window)

29.
S. M. Ulam, Problems in Modern Mathematics, Science Editions, Wiley, New York, 1964.