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Volume 2, Issue 2 (2013), Pages [61] - [107]
ON THE STABILITY OF QUADRATIC FUNCTIONAL EQUATION
[1] T. Aoki, On the stability of the linear transformation n Banach spaces, J. Math. Soc.
[2] B. Bouikhalene, E. Elqorachi and Th. M. Rassias, On the generalized Hyers-Ulam stability of the quadratic functional equation with a general involution, Nonlinear Funct. Anal. Appl. 12 (2007), 247-262.
[3] P. W. Cholewa, Remarks on the stability of functional equations, Aequationes Mathematicae 27(1-2) (1984), 76-86.
[4] St. Czerwik, On the stability of the quadratic mapping in normed spaces, Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg, 62 (1992), 59-64.
[5] L. Cadariu and V. Radu, Fixed points and the stability of Jensens functional equation, Journal of Inequalities in Pure and Applied Mathematics 4(1) (2003), Article 4.
[6] L. Cadariu and V. Radu, On the Stability of the Cauchy Functional Equation: A Fixed Point Approach, in Iteration Theory, Vol. 346 of Grazer Mathematische Berichte, pp. 43-52, Karl-Franzens-Universiteat Graz,
[7] A. Charifi, B. Bouikhalene and S. Kabbaj, Hyers-Ulam-Rassias, stability of additive functional equations, Nonlinear Functional Analysis and Applications (2007).
[8] J. B. Diaz and B. Margolis, A fixed point theorem of the alternative, for contractions on a generalized complete metric space, Bulletin of the American Mathematical Society 74 (1968), 305-309.
[9] P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, Journal of Mathematical Analysis and Applications 184(3) (1994), 431-436.
[10] D. H. Hyers, On the stability of the linear functional equation, Proceedings of the National Academy of Sciences of the United States of America 27(4) (1941), 222-224.
[11] G. Isac and Th. M. Rassias, Stability of additive mappings: Applications to nonlinear analysis, International Journal of Mathematics and Mathematical Sciences 19(2) (1996), 219-228.
[12] K. W. Jun and Y. H. Lee, On the Hyers-Ulam-Rassias stability of a pexiderized quadratic inequality, Mathematical Inequalities Applications, 4(1) (2001), 93-118.
[13] S. M. Jung, On the Hyers-Ulam stability of the functional equations that have the quadratic property, Journal of Mathematical Analysis and Applications 222(1) (1998), 126-137.
[14] S. M. Jung and P. K. Sahoo, Stability of a functional equation of Drygas, Aequationes Math. 64 (2002), 263-273.
[15] M. Mirzavaziri and M. S. Moslehian, A fixed point approach to stability of a quadratic equation, Bulletin of the Brazilian Mathematical Society 37(3) (2006), 361-376.
[16] A. Najati and C. Park, Fixed Points and Stability of a Generalized Quadratic Functional Equation, Hindawi Publishing Corporation, Journal of Inequalities and Applications, Volume 2009, Article ID 193035, 19 pages doi:10.1155/2009/193035.
[17] C. G. Park, On the stability of the quadratic mapping in Banach modules, Journal of Mathematical Analysis and Applications 276(1) (2002), 135-144.
[18] C. G. Park and Th. M. Rassias, Hyers-Ulam stability of a generalized Apollonius type quadratic mapping, Journal of Mathematical Analysis and Applications 322(1) (2006), 371-381.
[19] C. G. Park, On the stability of the quadratic mapping in Banach modules, Journal of Mathematical Analysis and Applications 276(1) (2002), 135-144.
[20] C. G. Park, Fixed points and Hyers-Ulam-Rassias stability of Cauchy-Jensen functional equations in Banach algebras, Fixed Point Theory and Applications, Vol. 2007, Article ID 50175, 15 pages, 2007.
[21] C. G. Park, Generalized Hyers-Ulam Stability of Quadratic Functional Equations: A Fixed Point Approach, Hindawi Publishing Corporation, Fixed Point Theory and Applications, Volume 2008.
[22] Th. M. Rassias, On the stability of linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.
[23] Th. M. Rassias, On the stability of functional equations in Banach spaces, Journal of Mathematical Analysis and Applications 251(1) (2000), 264-284.
[24] F. Skof, Local properties and approximation of operators, Rendiconti del Seminario Matematico e Fisico di Milano 53 (1983), 113-129.
[25] S. M. Ulam, Problems in Modern Mathematics, John Wiley and Sons,
[26] D. L. Yang, Remarks on the stability of Drygas equation and the Pexider-quadratic equation, Aequationes Math. 68 (2004), 108-116.