Local convergence radius for the Mann-type iteration

[1] I.K.Argyros, Concerning the radii of convergence for a certain class of Newton-like methods, J. Korea Math. Soc. Educ. Ser.B: Pure Appl. Math., 15, (2008), 47-55Search in Google Scholar

[2] I.K.Argyros, Concerning the ”terra incognita” between convergence regions of two Newton methods, Nonlinear Analysis, 62, (2005), 179-19410.1016/j.na.2005.02.113Search in Google Scholar

[3] O.P.Ferreira, Local convergence of Newtons method in Banach space from the viewpoint of the majorant principle, IMA J. of Numer. Anal., 29, (2009), 746-75910.1093/imanum/drn036Search in Google Scholar

[4] O.P.Ferreira, Local convergence of Newton’s method under a majorant condition in Riemannian manifolds, IMA Journal of Numerical Analysis, 32, (2012), 1696-171310.1093/imanum/drr048Search in Google Scholar

[5] O.P.Ferreira M.L.N.Goncalves, Local convergence analysis of inexact Newton-like methods under majorant condition, arXiv:0807.3903v1 [math.NA] 24 Jul, (2008)10.1007/s10589-009-9249-2Search in Google Scholar

[6] M. A. Hernández-Verón N. Romero, On the Local Convergence of a Third Order Family of Iterative Processes, Algorithms, 8, (2015), 1121-112810.3390/a8041121Search in Google Scholar

[7] L.B.Rall, A note on the convergence of Newton method, SIAM J. Numer. Anal., 11 No. 1, (1974), 34-3610.1137/0711004Search in Google Scholar

[8] H.Ren, On the local convergence of a deformed Newton’s method under Argyros-type condition, J. Math. Anal. Appl., 321, (2006), 396-40410.1016/j.jmaa.2005.08.057Search in Google Scholar

[9] W.C.Rheinboldt, An adaptive continuation process for solving systems of nonlinear equations, Polish Acad. Sci. Banach Center Publ., 3, (197), 129-14210.4064/-3-1-129-142Search in Google Scholar

[10] J.F.Traub H.Wozniakowski, Convergence and Complexity of Newton Iteration for Operator Equations, Journal of the Association for Computing Machinery, 26 No 2, (1979), 250-25810.1145/322123.322130Search in Google Scholar

[11] S.Smale, Complexity theory and numerical analysis, Acta Numer., 6, (1997), 523-55110.1017/S0962492900002774Search in Google Scholar

[12] X.Wang, Convergence of Newton’s method and uniquenees of the solution of equations in Banach space, IMA J.on Numer. Anal., 20, (2000), 123-13410.1093/imanum/20.1.123Search in Google Scholar