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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)
  • Received : 2012.09.13
  • Published : 2014.01.31

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.

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