{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,23]],"date-time":"2025-06-23T02:42:36Z","timestamp":1750646556735},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2016,9,13]],"date-time":"2016-09-13T00:00:00Z","timestamp":1473724800000},"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":[[2017,5]]},"DOI":"10.1007\/s11075-016-0203-y","type":"journal-article","created":{"date-parts":[[2016,9,13]],"date-time":"2016-09-13T01:20:16Z","timestamp":1473729616000},"page":"229-244","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Convergence of Steffensen\u2019s method for non-differentiable operators"],"prefix":"10.1007","volume":"75","author":[{"given":"I. K.","family":"Argyros","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M. A.","family":"Hern\u00e1ndez-Ver\u00f3n","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M. J.","family":"Rubio","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,9,13]]},"reference":[{"issue":"1","key":"203_CR1","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1016\/j.cam.2007.05.008","volume":"216","author":"V Alarc\u00f3n","year":"2008","unstructured":"Alarc\u00f3n, V., Amat, S., Busquier, S., L\u00f3pez, D. J.: A Steffensen\u2019s type method in Banach spaces with applications on boundary-value problems. J. Comput. Appl. Math. 216(1), 243\u2013250 (2008)","journal-title":"J. Comput. Appl. Math."},{"key":"203_CR2","first-page":"23","volume":"1","author":"IK Argyros","year":"1997","unstructured":"Argyros, I. K.: A new convergence theorem for Steffensen\u2019s method on Banach spaces and applications. Southwest J. Pure Appl. Math. 1, 23\u201329 (1997)","journal-title":"Southwest J. Pure Appl. Math."},{"issue":"3-4","key":"203_CR3","doi-asserted-by":"crossref","first-page":"223","DOI":"10.5486\/PMD.1993.1215","volume":"43","author":"I Argyros","year":"1993","unstructured":"Argyros, I.: On the Secant method. Publ. Math. Debrecen 43(3-4), 223\u2013238 (1993)","journal-title":"Publ. Math. Debrecen"},{"key":"203_CR4","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1007\/s11075-009-9271-6","volume":"52","author":"IK Argyros","year":"2009","unstructured":"Argyros, I. K., Ren, H: On an improved local convergence analysis for the Secant method. Numer. Algor. 52, 257\u2013271 (2009)","journal-title":"Numer. Algor."},{"key":"203_CR5","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1016\/0009-2509(77)80203-0","volume":"32","author":"DD Bruns","year":"1977","unstructured":"Bruns, D. D., Bailey, J. E.: Nonlinear feedback control for operating a nonisothermal CSTR near an unstable steady state. Chem. Eng. Sci. 32, 257\u2013264 (1977)","journal-title":"Chem. Eng. Sci."},{"key":"203_CR6","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1016\/j.amc.2006.10.014","volume":"188","author":"J Chen","year":"2007","unstructured":"Chen, J., Shen, Z.: Convergence analysis of the secant type methods. Appl. Math. Comput. 188, 514\u2013524 (2007)","journal-title":"Appl. Math. Comput."},{"key":"203_CR7","doi-asserted-by":"publisher","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":"203_CR8","doi-asserted-by":"publisher","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.: On Steffensen\u2019s method on Banach spaces. J. Comput. Appl. Math. 249, 9\u201323 (2013)","journal-title":"J. Comput. Appl. Math."},{"issue":"1-2","key":"203_CR9","doi-asserted-by":"publisher","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":"203_CR10","doi-asserted-by":"publisher","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 processes for solving nondifferentiable equations. J. Math. Anal. Appl. 275, 821\u2013834 (2002)","journal-title":"J. Math. Anal. Appl."},{"key":"203_CR11","doi-asserted-by":"publisher","unstructured":"Hern\u00e1ndez-Ver\u00f3n, M. A., Rubio, M. J.: On the ball of convergence of Secant-like methods for non-differentiable operators Applied Mathematics and Computation. doi: 10.1016\/j.amc.2015.10.007 (2015)","DOI":"10.1016\/j.amc.2015.10.007"},{"key":"203_CR12","doi-asserted-by":"publisher","first-page":"284","DOI":"10.1016\/j.cam.2005.07.008","volume":"194","author":"R Hongmin","year":"2006","unstructured":"Hongmin, R., Qingiao, W: The convergence ball of the Secant method under Hlder continuous divided differences. J. Comput. Appl. Math. 194, 284\u2013293 (2006)","journal-title":"J. Comput. Appl. Math."},{"issue":"3","key":"203_CR13","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1007\/s11766-007-0313-3","volume":"22","author":"L Kewei","year":"2007","unstructured":"Kewei, L.: Homocentric convergence ball of the Secant method. Appl. Math. J. Chinese Univ. Ser. B 22(3), 353\u2013365 (2007)","journal-title":"Appl. Math. J. Chinese Univ. Ser. B"},{"key":"203_CR14","unstructured":"Kung, H. T., Traub, J. F.: Optimal order of one-point and multipoint iteration Computer Science Department. Paper, 1747 (1973)"},{"key":"203_CR15","volume-title":"Nondiscrete induction and iterative methods","author":"FA Potra","year":"1984","unstructured":"Potra, F. A., Pt\u00e1k, V.: Nondiscrete induction and iterative methods. Pitman Publishing Limited, London (1984)"},{"key":"203_CR16","first-page":"251","volume":"9","author":"FA Potra","year":"1980","unstructured":"Potra, F. A.: A characterisation of the divided differences of an operator which can be represented by Riemann integrals. Anal. Numer. Theory Approx. 9, 251\u2013253 (1980)","journal-title":"Anal. Numer. Theory Approx."},{"key":"203_CR17","first-page":"147","volume":"185","author":"J Rashidinia","year":"2007","unstructured":"Rashidinia, J., Zarebnia, M.: New approach for numerical solution of Hammerstein integral equations. Appl. Math. Comput. 185, 147\u2013154 (2007)","journal-title":"Appl. Math. Comput."},{"key":"203_CR18","first-page":"7655","volume":"218","author":"H Ren","year":"2012","unstructured":"Ren, H., Argyros, I. K.: Local convergence of efficient Secant-type methods for solving nonlinear equations. Appl. Math. Comput. 218, 7655\u20137664 (2012)","journal-title":"Appl. Math. Comput."},{"key":"203_CR19","doi-asserted-by":"publisher","first-page":"2060083","DOI":"10.1002\/pamm.200701142","volume":"7","author":"S Shakhno","year":"2007","unstructured":"Shakhno, S.: On the Secant method under generalized Lipschitz conditions for the divided difference operator. PAMM-Proc. Appl. Math. Mech. 7, 2060083\u20132060084 (2007)","journal-title":"PAMM-Proc. Appl. Math. Mech."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-016-0203-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-016-0203-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-016-0203-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,19]],"date-time":"2024-06-19T09:48:56Z","timestamp":1718790536000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-016-0203-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,9,13]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,5]]}},"alternative-id":["203"],"URL":"https:\/\/doi.org\/10.1007\/s11075-016-0203-y","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,9,13]]}}}