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STABILITY OF ZEROS OF POWER SERIES EQUATIONS
Wang, Zhihua,Dong, Xiuming,Rassias, Themistocles M.,Jung, Soon-Mo Korean Mathematical Society 2014 대한수학회보 Vol.51 No.1
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.
Stability of zeros of power series equations
Zhihua Wang,Xiuming Dong,Themistocles M. Rassias,정순모 대한수학회 2014 대한수학회보 Vol.51 No.1
We prove that if |a1| is large and |a0| is small enough, then every approximate zero of power series equation P∞ n=0 anxn = 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, anzn + an−1zn−1 + · · · + a1z + a0 = 0 for a given integer n > 1.