caa a22 4500 463168968 CHVBK 20180406164807.0 cr unu---uuuuu 170326e20070501xx s 000 0 eng 10.1007/s10957-007-9197-x doi (NATIONALLICENCE)springer-10.1007/s10957-007-9197-x General Study of Iterative Processes of R -Order at Least Three under Weak Convergence Conditions [Elektronische Daten] [M. Hernández, N. Romero] We consider a family of Newton-type iterative processes solving nonlinear equations in Banach spaces, that generalizes the usually iterative methods of R-order at least three. The convergence of this family in Banach spaces is usually studied when the second derivative of the operator involved is Lipschitz continuous and bounded. In this paper, we relax the first condition, assuming that ‖F″(x)−F″(y)‖≤ω(‖x−y‖), where ω is a nondecreasing continuous real function. We prove that the different R-orders of convergence that we can obtain depend on the quasihomogeneity of the functionω. We end the paper by applying the study to some nonlinear integral equations. Springer Science+Business Media, LLC, 2007 Newton-type iterative processes nationallicence R -Order of convergence nationallicence Semilocal convergence nationallicence Hernández M. Department of Mathematics and Computation, University of La Rioja, Logroño, Spain aut Romero N. Department of Mathematics and Computation, University of La Rioja, Logroño, Spain aut Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 133/2(2007-05-01), 163-177 0022-3239 133:2<163 2007 133 10957 https://doi.org/10.1007/s10957-007-9197-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10957-007-9197-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hernández M. Department of Mathematics and Computation, University of La Rioja, Logroño, Spain aut NATIONALLICENCE 700 1- Romero N. Department of Mathematics and Computation, University of La Rioja, Logroño, Spain aut NATIONALLICENCE 773 0- Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 133/2(2007-05-01), 163-177 0022-3239 133:2<163 2007 133 10957 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer