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http://dx.doi.org/10.4134/BKMS.2014.51.1.077

STABILITY OF ZEROS OF POWER SERIES EQUATIONS  

Wang, Zhihua (School of Science Hubei University of Technology)
Dong, Xiuming (School of Science Hubei University of Technology)
Rassias, Themistocles M. (Department of Mathematics National Technical University of Athens)
Jung, Soon-Mo (Mathematics Section College of Science and Technology Hongik University)
Publication Information
Bulletin of the Korean Mathematical Society / v.51, no.1, 2014 , pp. 77-82 More about this Journal
Abstract
We prove that if ${\mid}a_1{\mid}$ is large and ${\mid}a_0{\mid}$ is small enough, then every approximate zero of power series equation ${\sum}^{\infty}_{n=0}a_nx^n$=0 can be approximated by a true zero within a good error bound. Further, we obtain Hyers-Ulam stability of zeros of the polynomial equation of degree n, $a_nz^n$ + $a_{n-1}z^{n-1}$ + ${\cdots}$ + $a_1z$ + $a_0$ = 0 for a given integer n > 1.
Keywords
Hyers-Ulam stability; power series equation; polynomial equation; zero;
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  • Reference
1 T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan 2 (1950), 64-66.   DOI
2 M. Bidkham, H. A. Soleiman Mezerji, and M. Eshaghi Gordji, Hyers-Ulam stability of polynomial equations, Abstr. Appl. Anal. 2010 (2010), Article ID 754120, 7 pages.
3 M. Bidkham, H. A. Soleiman Mezerji, and M. Eshaghi Gordji, Hyers-Ulam stability of power series equations, Abstr. Appl. Anal. 2011 (2011), Article ID 194948, 6 pages.
4 G. L. Forti, Hyers-Ulam stability of functional equations in several variables, Aequationes Math. 50 (1995), no. 1-2, 143-190.   DOI   ScienceOn
5 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
6 D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. U.S.A. 27 (1941), 222-224.   DOI   ScienceOn
7 D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of Functional Equations in Several variables, Birkhauser, Basel, 1998.
8 S.-M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis, Springer Optimization and Its Applications Vol. 48, Springer, New York, 2011.
9 S.-M. Jung, Hyers-Ulam stability of zeros of polynomial, Appl. Math. Lett. 24 (2011), no. 8, 1322-1325.   DOI   ScienceOn
10 Pl. Kannappan, Functional Equations and Inequalities with Applications, Springer, New York, 2009.
11 Y. Li and L. Hua, Hyers-Ulam stability of a polynomial equation, Banach J. Math. Anal. 3 (2009), no. 2, 86-90.   DOI
12 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
13 Th. M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Appl. Math. 62 (2000), no. 1, 23-130.   DOI   ScienceOn
14 Th. M. Rassias, Functional Equations, Inequalities and Applications, Kluwer Academic, Dordrecht, 2003.
15 E. Schechter, Handbook of Analysis and its Foundations, Academic Press, New York, 1997.
16 S. M. Ulam, Problems in Modern Mathematics, Chapter VI, Science Editions, Wiley, New York, 1964.