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Wu and Zhao[17] provided a semilocal convergence analysis for a Newton-type method on a Banach space setting following the ideas of Frontini and Sormani [9]-[11]. In this study first: we point out inconsistencies between the hypotheses of Theorem1 and the two examples given in [17], and then, we provide the proof in affine invariant form forth is result. Then, we also establish new conver-gence results with the following advantages over the ones in [17]: weaker hypotheses,and finer error estimates on the distances involved.
A numerical example is also provided to show that our results apply in cases otherfail[17].
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참고문헌 (17)
참고문헌 신청
Argyros, I.K. / 1992 / The midpoint method for solving nonlinear operator equa-tions in Banach space / Appl. Math. Lett. 5 : 7 ~ 9
Argyros, I.K. / 1993 / Results on the Chebyshev method in Banach spaces / Proyecciones 12 : 119 ~ 128
Argyros, I.K. / 1994 / On the midpoint iterative method for solving nonlinear operator equations in Banach space and its applications in integral equations / Rev. Anal. Numer
Argyros, I.K. / 1994 / The midpoint method in Banach spaces and the Ptak error estimates / Appl. Math. Comput. 62 : 1 ~ 15
Argyros, I.K. / 2003 / An improved error analysis for Newton-like methods under generalized conditions / J. Comput. Appl. Math. 157 : 169 ~ 185
Argyros, I.K. / 1993 / Results on the Chebyshev method in Banach spaces / Proyecciones 12 : 119 ~ 128
Argyros, I.K. / 1994 / On the midpoint iterative method for solving nonlinear operator equations in Banach space and its applications in integral equations / Rev. Anal. Numer
Argyros, I.K. / 1994 / The midpoint method in Banach spaces and the Ptak error estimates / Appl. Math. Comput. 62 : 1 ~ 15
Argyros, I.K. / 2003 / An improved error analysis for Newton-like methods under generalized conditions / J. Comput. Appl. Math. 157 : 169 ~ 185
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