{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:15:05Z","timestamp":1758824105004},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2009,6,30]],"date-time":"2009-06-30T00:00:00Z","timestamp":1246320000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2009,12]]},"DOI":"10.1007\/s11075-009-9308-x","type":"journal-article","created":{"date-parts":[[2009,6,29]],"date-time":"2009-06-29T06:57:39Z","timestamp":1246258659000},"page":"701-726","source":"Crossref","is-referenced-by-count":9,"title":["On the convergence of Newton-type methods under mild differentiability conditions"],"prefix":"10.1007","volume":"52","author":[{"given":"Ioannis K.","family":"Argyros","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sa\u00efd","family":"Hilout","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2009,6,30]]},"reference":[{"key":"9308_CR1","unstructured":"Argyros, I.K.: The theory and application of abstract polynomial equations. Mathematics Series. St. Lucie\/CRC\/Lewis, Boca Raton (1998)"},{"key":"9308_CR2","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/j.cam.2004.01.029","volume":"169","author":"IK Argyros","year":"2004","unstructured":"Argyros, I.K.: On the Newton\u2013Kantorovich hypothesis for solving equations. J. Comput. Appl. Math. 169, 315\u2013332 (2004)","journal-title":"J. Comput. Appl. Math."},{"key":"9308_CR3","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1016\/j.jmaa.2004.04.008","volume":"298","author":"IK Argyros","year":"2004","unstructured":"Argyros, I.K.: A unifying local\u2013semilocal convergence analysis and applications for two-point Newton\u2013like methods in Banach space. J. Math. Anal. Appl. 298, 374\u2013397 (2004)","journal-title":"J. Math. Anal. Appl."},{"key":"9308_CR4","volume-title":"Convergence and applications of Newton\u2013type iterations","author":"IK Argyros","year":"2008","unstructured":"Argyros, I.K.: Convergence and applications of Newton\u2013type iterations. Springer, New York (2008)"},{"key":"9308_CR5","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.cam.2008.08.042","volume":"228","author":"IK Argyros","year":"2009","unstructured":"Argyros, I.K.: On a class of Newton-like methods for solving nonlinear equations. J. Comput. Appl. Math. 228, 115\u2013122 (2009)","journal-title":"J. Comput. Appl. Math."},{"key":"9308_CR6","volume-title":"Radiative transfer","author":"S Chandrasekhar","year":"1960","unstructured":"Chandrasekhar, S.: Radiative transfer. Dover, New York (1960)"},{"key":"9308_CR7","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1007\/BF00050844","volume":"42","author":"X Chen","year":"1990","unstructured":"Chen, X.: On the convergence of Broyden-like methods for nonlinear equations with nondifferentiable terms. Ann. Inst. Stat. Math. 42, 387\u2013401 (1990)","journal-title":"Ann. Inst. Stat. Math."},{"key":"9308_CR8","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1080\/01630568908816289","volume":"10","author":"X Chen","year":"1989","unstructured":"Chen, X., Yamamoto, T.: Convergence domains of certain iterative methods for solving nonlinear equations. Numer. Funct. Anal. Optim. 10, 37\u201348 (1989)","journal-title":"Numer. Funct. Anal. Optim."},{"key":"9308_CR9","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1081\/NFA-120026367","volume":"24","author":"F Cianciaruso","year":"2003","unstructured":"Cianciaruso, F., De Pascale, E.: Newton\u2013Kantorovich aproximations when the derivative is H\u00f6lderian: old and new results. Numer. Funct. Anal. Optim. 24, 713\u2013723 (2003)","journal-title":"Numer. Funct. Anal. Optim."},{"key":"9308_CR10","unstructured":"Cianciaruso, F.: A further journey in the \u201cterra incognita\u201d of the Newton\u2013Kantorovich method. Nonlinear Funct. Anal. Appl. (2009, in press)"},{"key":"9308_CR11","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1016\/B978-0-12-576350-9.50010-2","volume-title":"Nonlinear Functional Analysis and Applications","author":"JE Dennis","year":"1971","unstructured":"Dennis, J.E.: Toward a unified convergence theory for Newton\u2013like methods. In: Rall, L.B. (ed.) Nonlinear Functional Analysis and Applications, pp. 425\u2013472. Academic, New York (1971)"},{"key":"9308_CR12","series-title":"Springer Series in Computational Mathematics","volume-title":"Affine Invariance and Adaptive Algorithms","author":"P Deuflhard","year":"2004","unstructured":"Deuflhard, P.: Newton methods for nonlinear problems. In: Affine Invariance and Adaptive Algorithms. Springer Series in Computational Mathematics, vol. 35. Springer, Berlin (2004)"},{"key":"9308_CR13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/0716001","volume":"16","author":"P Deuflhard","year":"1979","unstructured":"Deuflhard, P., Heindl, G.: Affine invariant convergence theorems for Newton\u2019s method and extensions to related methods. SIAM J. Numer. Anal. 16, 1\u201310 (1979)","journal-title":"SIAM J. Numer. Anal."},{"key":"9308_CR14","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/S0377-0427(97)81611-1","volume":"79","author":"JM Guti\u00e9rrez","year":"1997","unstructured":"Guti\u00e9rrez, J.M.: A new semilocal convergence theorem for Newton\u2019s method. J. Comput. Appl. Math. 79, 131\u2013145 (1997)","journal-title":"J. Comput. Appl. Math."},{"issue":"3","key":"9308_CR15","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1023\/A:1017571906739","volume":"109","author":"MA Hern\u00e1ndez","year":"2001","unstructured":"Hern\u00e1ndez, M.A.: The Newton method for operators with H\u00f6lder continuous first derivatives. J. Optim. Theory Appl. 109(3), 631\u2013648 (2001)","journal-title":"J. Optim. Theory Appl."},{"key":"9308_CR16","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/S0377-0427(99)00116-8","volume":"115","author":"MA Hern\u00e1ndez","year":"2000","unstructured":"Hern\u00e1ndez, M.A., Rubio, M.J., Ezquerro, J.A.: Secant-like methods for slving nonlinear integral equations of the Hammerstein type. J. Comput. Appl. Math. 115, 245\u2013254 (2000)","journal-title":"J. Comput. Appl. Math."},{"key":"9308_CR17","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/0377-0427(93)90004-U","volume":"47","author":"Z Huang","year":"1993","unstructured":"Huang, Z.: A note of Kantorovich theorem for Newton iteration. J. Comput. Appl. Math. 47, 211\u2013217 (1993)","journal-title":"J. Comput. Appl. Math."},{"key":"9308_CR18","volume-title":"Functional analysis","author":"LV Kantorovich","year":"1982","unstructured":"Kantorovich, L.V., Akilov, G.P.: Functional analysis. Pergamon, Oxford (1982)"},{"key":"9308_CR19","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1007\/BF01399322","volume":"33","author":"GJ Miel","year":"1979","unstructured":"Miel, G.J.: Unified error analysis for Newton\u2013type methods. Numer. Math. 33, 391\u2013396 (1979)","journal-title":"Numer. Math."},{"key":"9308_CR20","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1090\/S0025-5718-1980-0551297-4","volume":"34","author":"GJ Miel","year":"1980","unstructured":"Miel, G.J.: Majorizing sequences and error bounds for iterative methods. Math. Comput. 34, 185\u2013202 (1980)","journal-title":"Math. Comput."},{"key":"9308_CR21","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/BF02243076","volume":"33","author":"I Moret","year":"1984","unstructured":"Moret, I.: A note on Newton type iterative methods. Computing 33, 65\u201373 (1984)","journal-title":"Computing"},{"key":"9308_CR22","first-page":"71","volume":"5","author":"FA Potra","year":"1985","unstructured":"Potra, F.A.: Sharp error bounds for a class of Newton\u2013like methods. Libertas Mathematica 5, 71\u201384 (1985)","journal-title":"Libertas Mathematica"},{"key":"9308_CR23","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1137\/0705003","volume":"5","author":"WC Rheinboldt","year":"1968","unstructured":"Rheinboldt, W.C.: A unified convergence theory for a class of iterative processes. SIAM J. Numer. Anal. 5, 42\u201363 (1968)","journal-title":"SIAM J. Numer. Anal."},{"key":"9308_CR24","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1007\/BF01400355","volume":"51","author":"T Yamamoto","year":"1987","unstructured":"Yamamoto, T.: A convergence theorem for Newton\u2013like methods in Banach spaces. Numer. Math. 51, 545\u2013557 (1987)","journal-title":"Numer. Math."},{"key":"9308_CR25","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1080\/01630568708816254","volume":"9","author":"PP Zabrejko","year":"1987","unstructured":"Zabrejko, P.P., Nguen, D.F.: The majorant method in the theory of Newton\u2013Kantorovich approximations and the Pt\u00e1k error estimates. Numer. Funct. Anal. Optim. 9, 671\u2013684 (1987)","journal-title":"Numer. Funct. Anal. Optim."},{"key":"9308_CR26","unstructured":"Zinc\u0306enko, A.I.: Some approximate methods of solving equations with non-differentiable operators. (Ukrainian), Dopovidi Akad, pp. 156\u2013161. Nauk Ukra\u00efn. RSR (1963)"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-009-9308-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-009-9308-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-009-9308-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T05:08:14Z","timestamp":1559365694000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-009-9308-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,6,30]]},"references-count":26,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2009,12]]}},"alternative-id":["9308"],"URL":"https:\/\/doi.org\/10.1007\/s11075-009-9308-x","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,6,30]]}}}