# ON THE STABILITY OF INVOLUTIVE A-QUADRATIC MAPPINGS

• Park, Won-Gil (NATIONAL INSTITUTE FOR MATHEMATICAL SCIENCES) ;
• Bae, Jae-Hyeong (DEPARTMENT OF MATHEMATICS AND APPLIED MATHEMATICS, KYUNGHEE UNIVERSITY)
• Published : 2006.11.30

#### Abstract

In this paper, we will investigate the Hyers-Ulam stability of an involutive A-quadratic mapping.

#### References

1. J. Aczel and J. Dhombres, Functional equations in several variables, Cambridge Univ. Press, Cambridge, 1989
2. J.-H. Bae and K.-W. Jun, On the generalized Hyers-Ulam-Rassias stability of an n-dimensional quadratic functional equation, J. Math. Anal. Appl. 258 (2001), no. 1, 183-193 https://doi.org/10.1006/jmaa.2000.7372
3. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer-Verlag New York, Heidelberg and Berlin, 1973
4. S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg. 62 (1992), 59-64 https://doi.org/10.1007/BF02941618
5. P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approxi-mately additive mappings, J. Math. Anal. Appl. 184 (1994), no. 3, 431-436 https://doi.org/10.1006/jmaa.1994.1211
6. D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A. 27 (1941), 222-224
7. K.-W. Jun, J.-H. Bae, and Y.-H. Lee, On the Hyers-Ulam-Rassias stability of ann-dimensional Pexiderized quadratic equation, Math. Ineq. Appl. 7 (2004), no. 1, 63-77
8. K.-W. Jun, J.-H. Bae, and W.-G. Park, Partitioned functional inequalities in Banach modules and approximate algebra homomorphisms, Math. Ineq. Appl. 6 (2003), no. 4, 715-726
9. D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Basel-Boston, 1998
10. R. Kadison and G. Pedersen, Means and convex combinations of unitary operators, Math. Scand. 57 (1985), no. 2, 249-266 https://doi.org/10.7146/math.scand.a-12116
11. C.-G. Park, Functional equations in Banach modules, Indian J. Pure Appl. Math. 33 (2002), no. 7, 1077-1086
12. C.-G. Park, Multilinear mappings in Banach modules over a $C^{*}$-algebra, Indian J. Pure Appl. Math., to appear
13. C.-G. Park and J.-K. Shin, Generalized Jensens equations in Banach modules, Indian J. Pure Appl. Math. 33 (2002), no. 12, 1867-1875
14. Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300
15. F. Skof, Local properties and approximation of operators, Rend. Sem. Mat. Fis. Milano 53 (1983), 113-129 https://doi.org/10.1007/BF02924890
16. S. M. Ulam, Problems in Modern Mathematics, Wiley, New York, 1964
17. J. Vukman, Some functional equations in Banach algebras and an application, Proc. Amer. Math. Soc. 100 (1987), no. 1, 133-136