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http://dx.doi.org/10.4134/BKMS.2005.42.1.133

ON THE HYERS-ULAM STABILITY OF A GENERALIZED QUADRATIC AND ADDITIVE FUNCTIONAL EQUATION  

JUN, KIL-WOUNG (Department of Mathematics, Chung-nam National University)
KIM, HARK-MAHN (Department of Mathematics, Chung-nam National University)
Publication Information
Bulletin of the Korean Mathematical Society / v.42, no.1, 2005 , pp. 133-148 More about this Journal
Abstract
In this paper, we obtain the general solution of a gen-eralized quadratic and additive type functional equation f(x + ay) + af(x - y) = f(x - ay) + af(x + y) for any integer a with a $\neq$ -1. 0, 1 in the class of functions between real vector spaces and investigate the generalized Hyers- Ulam stability problem for the equation.
Keywords
Hyers-Ulam stability; quadratic function;
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1 D. H. Hyers, On the asymptoticity aspect of Hyers- Ulam stability of mappings, Proc. Amer. Math. Soc. 126 (1998), 425-430
2 J. Aczel and J. Dhombres, Functional Equations in Several Variables, Cambridge Univ. Press, 1989
3 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), 183-193   DOI   ScienceOn
4 J. Baker, The stability of the cosine equation, Proc. Amer. Math. Soc. 80 (1980), 411-416
5 I. S. Chang and H. M. Kim, On the Hyers-Ulam stability of quadratic functional equations, J. Inequal. Appl. 3 (2002), no. 3
6 S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg 62 (1992), 59-64   DOI
7 D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA 27 (1941), 222-224
8 K. W. Jun and H. M. Kim, Remarks on the stability of additive functional equation, Bull. Korean Math. Soc. 38 (2001), 679-687
9 K. W. Jun and Y. H. Lee, On the Hyers-Ulam-Rassias stability of a generalized quadratic equation, Bull. Korean Math. Soc. 38 (2001), 261-272
10 S. -M. Jung, On the Hyers- Ulam stability of the functional equations that have the quadratic property, J. Math. Anal. Appl. 222 (1998), 126-137   DOI   ScienceOn
11 Th. M. Rassias, Inner product spaces and applications, Nongman, 1997
12 Th. M. Rassias, On the stability of functional equations in Banach spaces, J. Math. Anal. Appl. 251 (2000), 264-284   DOI   ScienceOn
13 Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300
14 S. M. Ulam, Problems in Modern Mathematics, Chap. VI, Science ed. Wiley, New York, 1964
15 P. Giivruta, A generalization of the Hyers- Ulam-Rassias Stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), 431-436   DOI   ScienceOn
16 D. H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992), 125-153   DOI
17 D. H. Hyers, G. Isac, and Th. M. Rassias, 'Stability of FUnctional Equations in Several Variables', Birkhauser, Basel, 1998
18 K. W. Jun, On the Hyers- Ulam-Rassias stability of a pexiderized quadratic inequality, Math. Inequal. Appl. 4 (2001), no. 1, 93-118