{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,12,20]],"date-time":"2023-12-20T14:41:37Z","timestamp":1703083297088},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2016,9,22]],"date-time":"2016-09-22T00:00:00Z","timestamp":1474502400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2017,7]]},"DOI":"10.1007\/s11075-016-0211-y","type":"journal-article","created":{"date-parts":[[2016,9,22]],"date-time":"2016-09-22T01:02:59Z","timestamp":1474506179000},"page":"553-567","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On the convergence of Newton-like methods using restricted domains"],"prefix":"10.1007","volume":"75","author":[{"given":"Ioannis K.","family":"Argyros","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Santhosh","family":"George","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,9,22]]},"reference":[{"key":"211_CR1","doi-asserted-by":"crossref","unstructured":"Amat, S., Busquier S., Guti\u00e9rrez, J.M.: Geometric constructions of iterative functions to solve nonlinear equations, vol. 157 (2003)","DOI":"10.1016\/S0377-0427(03)00420-5"},{"issue":"1","key":"211_CR2","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.amc.2008.08.050","volume":"206","author":"S Amat","year":"2008","unstructured":"Amat, S., Hern\u00e1ndez, M.A., Romero, N.: A modified Chebyshev\u2019s iterative method with at least sixth order of convergence. Appl. Math. Comput. 206(1), 164\u2013174 (2008)","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"211_CR3","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.jmaa.2007.02.052","volume":"336","author":"S Amat","year":"2007","unstructured":"Amat, S., Busquier, S.: Third order iterative methods under Kantorovich conditions. J. Math. Anal. Appl. 336(1), 243\u2013261 (2007)","journal-title":"J. Math. Anal. Appl."},{"key":"211_CR4","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1007\/s00010-004-2733-y","volume":"69","author":"S Amat","year":"2005","unstructured":"Amat, S., Busquier, S., Plaza, S.: Dynamics of the King\u2019s and Jarratt iterations. Aequationes Math. 69, 212\u2013213 (2005)","journal-title":"Aequationes Math."},{"key":"211_CR5","doi-asserted-by":"crossref","unstructured":"Amat, S., Busquier, S., Plaza, S.: Chaotic of a third-order Newton-type method. J. Math. Anal. Appl. 366(1), 24\u201332","DOI":"10.1016\/j.jmaa.2010.01.047"},{"issue":"9","key":"211_CR6","doi-asserted-by":"crossref","first-page":"2936","DOI":"10.1016\/j.cam.2010.12.011","volume":"235","author":"S Amat","year":"2011","unstructured":"Amat, S., Busquier, S., Gutierrez, J.M.: Third order iterative methods with applications to Hammerstein equations: a unified approach. J. Comput. Appl. Math. 235(9), 2936\u20132943 (2011)","journal-title":"J. Comput. Appl. Math."},{"key":"211_CR7","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.cam.2007.07.022","volume":"220","author":"S Amat","year":"2009","unstructured":"Amat, S., Busquier, S., Gutierrez, J.M., Hern\u00e1ndez, M.A., Romero, N.: On the global convergence of Chebyshev\u2019s iterative method. J. Comput. Appl. Math. 220, 17\u201321 (2009)","journal-title":"J. Comput. Appl. Math."},{"key":"211_CR8","unstructured":"Argyros, I.K.: The theory and application of abstract polynomial equations, St Lucie\/CRC\/Lewis Publ. Mathematics Series, Boca Raton, FL, USA (1998)"},{"key":"211_CR9","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-Kantorovich hypothesis for solving equations. J. Comput. Appl. Math. 169, 315\u2013332 (2004)","journal-title":"J. Comput. Appl. Math."},{"key":"211_CR10","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-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space. J. Math. Anal. Appl 298, 374\u2013397 (2004)","journal-title":"J. Math. Anal. Appl"},{"key":"211_CR11","volume-title":"Series: Studies in Computational Mathematicsm, vol. 15","author":"IK Argyros","year":"2007","unstructured":"Argyros, I.K.: Computational theory of iterative methods. In: Chui, C.K., Wuytack, L. (eds.) Series: Studies in Computational Mathematics, vol. 15. Elsevier Publ. Co, New York (2007)"},{"key":"211_CR12","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":"211_CR13","volume-title":"Radiative transfer","author":"S Chandrasekhar","year":"1960","unstructured":"Chandrasekhar, S.: Radiative transfer. Dover Publications, New York (1960)"},{"key":"211_CR14","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":"211_CR15","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-00547-7","volume-title":"Nonlinear functional analysis","author":"K Deimling","year":"1985","unstructured":"Deimling, K.: Nonlinear functional analysis. Springer-Verlag, Berlin (1985)"},{"key":"211_CR16","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-like methods. In: Rall, L.B. (ed.) Nonlinear Functional Analysis and Applications, pp 425\u2013472. Academic Press, New York (1971)"},{"key":"211_CR17","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 Newtons method and extensions to related methods. SIAM J. Numer. Anal 16, 1\u201310 (1979)","journal-title":"SIAM J. Numer. Anal"},{"issue":"2","key":"211_CR18","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/s002459911012","volume":"41","author":"JA Ezquerro","year":"2000","unstructured":"Ezquerro, J.A., Hern\u00e1ndez, M.A.: Recurrence relations for Chebyshev-type method. App. MAth. Optim. 41(2), 227\u2013236 (2000)","journal-title":"App. MAth. Optim."},{"key":"211_CR19","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.cam.2013.02.004","volume":"249","author":"JA Ezquerro","year":"2013","unstructured":"Ezquerro, J.A., Hern\u00e1ndez, M.A., Romero, N., Velasco, A.I.: On steffensen\u2019s method on Banach spaces. J. Comput. Appl. Math. 249, 9\u201323 (2013)","journal-title":"J. Comput. Appl. Math."},{"key":"211_CR20","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1016\/j.jmaa.2004.08.057","volume":"303","author":"JA Ezquerro","year":"2005","unstructured":"Ezquerro, J.A., Hern\u00e1ndez, M.A.: On the R-order of the Halley method. J. Math. Anal. Appl 303, 591\u2013601 (2005)","journal-title":"J. Math. Anal. Appl"},{"key":"211_CR21","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/s10543-009-0226-z","volume":"49","author":"JA Ezquerro","year":"2009","unstructured":"Ezquerro, J.A., Hern\u00e1ndez, M.A.: New iterations of R-order four with reduced computational cost. BIT Numer. Math. 49, 325\u2013342 (2009)","journal-title":"BIT Numer. Math."},{"key":"211_CR22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/imanum\/11.1.21","volume":"11","author":"M Ganesh","year":"1991","unstructured":"Ganesh, M., Joshi, M.C.: Numerical solvability of Hammerstein integral equations of mixed type. IMA J. Numer. Anal. 11, 1\u20138 (1991)","journal-title":"IMA J. Numer. Anal."},{"issue":"7","key":"211_CR23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0898-1221(98)00168-0","volume":"36","author":"JM Guti\u00e9rrez","year":"1998","unstructured":"Guti\u00e9rrez, J.M., Hern\u00e1ndez, M.A.: Recurrence relations for the super-Halley method. Comput. Math. Appl. 36(7), 1\u20138 (1998)","journal-title":"Comput. Math. Appl."},{"issue":"3-4","key":"211_CR24","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1016\/S0898-1221(00)00286-8","volume":"41","author":"MA Hern\u00e1ndez","year":"2001","unstructured":"Hern\u00e1ndez, M.A.: Chebyshev\u2019s approximation algorithms and applications. Comput. Math. Appl. 41(3-4), 433\u2013455 (2001)","journal-title":"Comput. Math. Appl."},{"key":"211_CR25","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1016\/S0022-247X(02)00432-8","volume":"275","author":"MA Hern\u00e1ndez","year":"2002","unstructured":"Hern\u00e1ndez, M.A., Rubio, M.J.: A uniparametric family of iterative process for solving nondifferentiable equations. J. Math. Anal. Appl. 275, 821\u2013834 (2002)","journal-title":"J. Math. Anal. Appl."},{"issue":"15","key":"211_CR26","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1016\/j.amc.2015.10.007","volume":"273","author":"MA Hern\u00e1ndez","year":"2016","unstructured":"Hern\u00e1ndez, M.A., Rubio, M.J.: On the ball of convergence of Secant-like methods for nondifferentiable operators. Appl. Math. Comput. 273(15), 506\u2013512 (2016)","journal-title":"Appl. Math. Comput."},{"issue":"1-2","key":"211_CR27","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 solving nonlinear integral equations of the Hammerstein type. J. Comput. Appl. Math. 115(1-2), 245\u2013254 (2000)","journal-title":"J. Comput. Appl. Math."},{"key":"211_CR28","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1016\/j.mcm.2003.12.013","volume":"41","author":"C Ma","year":"2005","unstructured":"Ma, C.: A smoothing Broyden-like method for the mixed complementarity problems. Math. Comput. Model. 41, 523\u2013538 (2005)","journal-title":"Math. Comput. Model."},{"key":"211_CR29","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/j.amc.2014.09.061","volume":"248","author":"AA Magren\u00e1n","year":"2014","unstructured":"Magren\u00e1n, A.A.: A new tool to study real dynamics: the convergence plane. Appl. Math. Comput. 248, 215\u2013225 (2014)","journal-title":"Appl. Math. Comput."},{"key":"211_CR30","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-type methods. Numer. Math. 33, 391\u2013396 (1979)","journal-title":"Numer. Math."},{"key":"211_CR31","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. Comp. 34, 185\u2013202 (1980)","journal-title":"Math. Comp."},{"key":"211_CR32","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":"211_CR33","first-page":"71","volume":"5","author":"FA Potra","year":"1985","unstructured":"Potra, F.A.: Sharp error bounds for a class of Newton-like methods. Libertas Math. 5, 71\u201384 (1985)","journal-title":"Libertas Math."},{"key":"211_CR34","volume-title":"Nondiscrete induction and iterative processes, Research Notes in Mathematics, vol. 103","author":"FA Potra","year":"1984","unstructured":"Potra, F.A., Pt\u00e1k, V.: Nondiscrete induction and iterative processes, Research Notes in Mathematics, vol. 103. Pitman Publ, Boston (1984)"},{"key":"211_CR35","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":"211_CR36","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-like methods in Banach spaces. Numer. Math. 51, 545\u2013557 (1987)","journal-title":"Numer. Math."},{"key":"211_CR37","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-Kantorovich approximations and the Pt\u00e1k error estimates. Numer. Funct. Anal. Optim 9, 671\u2013684 (1987)","journal-title":"Numer. Funct. Anal. Optim"},{"key":"211_CR38","unstructured":"Zincenko, A.I.: Some approximate methods of solving equations with non-differentiable operators, (Ukrainian), Dopovidi Akad. Nauk Ukran. RSR (1963)"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-016-0211-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-016-0211-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-016-0211-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,26]],"date-time":"2020-09-26T05:31:59Z","timestamp":1601098319000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-016-0211-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,9,22]]},"references-count":38,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,7]]}},"alternative-id":["211"],"URL":"https:\/\/doi.org\/10.1007\/s11075-016-0211-y","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,9,22]]}}}