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Also, the relevant results on premises of Kantorovich and Smale types are improved in this paper.<\/p>","DOI":"10.1090\/s0025-5718-99-00999-0","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:28Z","timestamp":1027707268000},"page":"169-186","source":"Crossref","is-referenced-by-count":99,"title":["Convergence of Newton\u2019s method and inverse function theorem in Banach space"],"prefix":"10.1090","volume":"68","author":[{"given":"Wang","family":"Xinghua","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[1999]]},"reference":[{"key":"1","unstructured":"[1] Wang Xinghua, Convergence of Newton\u2019s method and uniqueness of the solution of equations in Banach space, Hangzhou University, preprint."},{"key":"2","isbn-type":"print","volume-title":"Functional analysis","author":"Kantorovich, L. V.","year":"1982","ISBN":"https:\/\/id.crossref.org\/isbn\/0080230369","edition":"2"},{"key":"3","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1137\/0711002","article-title":"Optimal error bounds for the Newton-Kantorovich theorem","volume":"11","author":"Gragg, W. B.","year":"1974","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"key":"4","series-title":"Pure and Applied Mathematics, Vol. 9","volume-title":"Solution of equations in Euclidean and Banach spaces","author":"Ostrowski, A. M.","year":"1973"},{"key":"5","unstructured":"[5] Wang Xinghua, Convergence of an iterative procedure, KeXue TongBao, 20(1975), 558-559; J. of Hangzhou University, 1977, 2: 16-42; 1978, 3: 23-26."},{"issue":"12","key":"6","first-page":"125","article-title":"On the a posteriori error estimates for Newton\u2019s method","author":"Potra, Florian Alexandru","year":"1984","journal-title":"Beitr\\\"{a}ge Numer. 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A","ISSN":"https:\/\/id.crossref.org\/issn\/1001-6511","issn-type":"print"},{"key":"10","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-2740-3","volume-title":"From Topology to Computation: Proceedings of the Smalefest","year":"1993","ISBN":"https:\/\/id.crossref.org\/isbn\/0387979328"},{"key":"11","series-title":"Contemporary Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/163","volume-title":"Computational mathematics in China","volume":"163","year":"1994","ISBN":"https:\/\/id.crossref.org\/isbn\/0821851632"},{"issue":"1","key":"12","first-page":"47","article-title":"Domain estimates and point estimates for Newton iteration","volume":"12","author":"Wang, Xing Hua","year":"1990","journal-title":"Math. Numer. Sinica","ISSN":"https:\/\/id.crossref.org\/issn\/0254-7791","issn-type":"print"},{"issue":"6","key":"13","first-page":"721","article-title":"Convergence of Euler\u2019s series, Euler\u2019s iterative family and Halley\u2019s iterative family under a point estimate criterion","volume":"33","author":"Wang, Xing Hua","year":"1990","journal-title":"Acta Math. Sinica","ISSN":"https:\/\/id.crossref.org\/issn\/0583-1431","issn-type":"print"},{"key":"14","unstructured":"[14] Wang Xinghua and Han Danfu, The convergence of Euler\u2019s series and combinatorial skills, preprint, Hangzhou University, 1996."},{"key":"15","unstructured":"[15] L. Blum, F. Cucker, M. Shub and S. Smale, Complexity and Real Computation, Part II: Some Geometry of Numerical Algorithms, City University of Hong Kong, preprint, 1996."},{"issue":"207","key":"16","doi-asserted-by":"publisher","first-page":"247","DOI":"10.2307\/2153572","article-title":"Approximate zeros of quadratically convergent algorithms","volume":"63","author":"Chen, Pengyuan","year":"1994","journal-title":"Math. 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