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http://dx.doi.org/10.4134/BKMS.2008.45.2.397

ON THE STABILITY OF THE MONOMIAL FUNCTIONAL EQUATION  

Lee, Yang-Hi (Department of Mathematics Education Gongju National University of Education)
Publication Information
Bulletin of the Korean Mathematical Society / v.45, no.2, 2008 , pp. 397-403 More about this Journal
Abstract
In this paper, we modify L. $C\breve{a}dariu$ and V. Radu's result for the stability of the monomial functional equation $\sum\limits_{n=0}^{n}n\;C_i(-1)^{n-i}f(ix+y)-n!f(x)=0$ in the sense of Th. M. Rassias. Also, we investigate the superstability of the monomial functional equation.
Keywords
stability; monomial functional equation;
Citations & Related Records

Times Cited By Web Of Science : 7  (Related Records In Web of Science)
Times Cited By SCOPUS : 12
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1 P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), no. 3, 431-436   DOI   ScienceOn
2 K.-W. Jun and Y.-H. Lee, On the Hyers-Ulam-Rassias stability of a Pexiderized quadratic inequality, Math. Inequal. Appl. 4 (2001), no. 1, 93-118
3 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
4 P. W. Cholewa, Remarks on the stability of functional equations, Aequationes Math. 27 (1984), no. 1-2, 76-86   DOI
5 S. Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific Publishing Co., Inc., River Edge, NJ, 2002
6 S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg 62 (1992), 59-64   DOI
7 Z. Gajda, On stability of additive mappings, Internat. J. Math. Math. Sci. 14 (1991), no. 3, 431-434   DOI   ScienceOn
8 D. H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992), no. 2-3, 125-153   DOI
9 S.-M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Inc., Palm Harbor, FL, 2001
10 S.-M. Jung, On the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 204 (1996), no. 1, 221-226   DOI   ScienceOn
11 H.-M. Kim, On the stability problem for a mixed type of quartic and quadratic functional equation, J. Math. Anal. Appl. 324 (2006), no. 1, 358-372   DOI   ScienceOn
12 J. M. Rassias, Solution of the Ulam stability problem for cubic mappings, Glas. Mat. Ser. III 36(56) (2001), no. 1, 63-72
13 Th. M. Rassias, On a modified Hyers-Ulam sequence, J. Math. Anal. Appl. 158 (1991), no. 1, 106-113   DOI
14 D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A. 27 (1941), 222-224   DOI   ScienceOn
15 D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of functional equations in several variables, Progress in Nonlinear Differential Equations and their Applications, 34. Birkhauser Boston, Inc., Boston, MA, 1998
16 Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300   DOI   ScienceOn
17 Th. M. Rassias, Report of the 27th International Symposium on Functional Equations, Aeq. Math. 39 (1990), 292-293
18 Th. M. Rassias, The problem of S. M. Ulam for approximately multiplicative mappings, J. Math. Anal. Appl. 246 (2000), no. 2, 352-378   DOI   ScienceOn
19 Th. M. Rassias, Functional Equations and Inequalities, Mathematics and its Applications, 518. Kluwer Academic Publishers, Dordrecht, 2000
20 Th. M. Rassias, Functional Equations, Inequalities and Applications, Kluwer Academic Publishers, Dordrecht, 2003
21 F. Skof, Local properties and approximation of operators, Rend. Sem. Mat. Fis. Milano 53 (1983), 113-129   DOI
22 Th. M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Appl. Math. 62 (2000), no. 1, 23-130   DOI
23 Y.-H. Lee and K.-W. Jun, On the stability of approximately additive mappings, Proc. Amer. Math. Soc. 128 (2000), no. 5, 1361-1369   DOI   ScienceOn
24 J. M. Rassias, Solution of the Ulam stability problem for quartic mappings, Glas. Mat. Ser. III 34(54) (1999), no. 2, 243-252
25 Th. M. Rassias, On the stability of functional equations in Banach spaces, J. Math. Anal. Appl. 251 (2000), no. 1, 264-284   DOI   ScienceOn
26 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   DOI   ScienceOn
27 S. M. Ulam, A Collection of Mathematical Problems, Interscience Tracts in Pure and Applied Mathematics, no. 8 Interscience Publishers, New York-London, 1960