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Strong convergence of the Ishikawa iteration for Lipschitz α-hemicontractive mappings


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[1] T.L. Hicks and J.D. Kubicek, On the Mann iteration process in a Hilbert spaces, J. Math. Anal. Appl., 59, (1977), 498-50410.1016/0022-247X(77)90076-2Search in Google Scholar

[2] Ș. Mărușter, Sur le calcul des zeros d'un operateur discontinu par iteration, Canad. Math. Bull., 16 (4), (1973), 541-54410.4153/CMB-1973-088-7Search in Google Scholar

[3] Ș. Mărușter, The solution by iteration of nonlinear equations in Hilbert spaces, Proc. Amer. Math Soc., 63 (1), (1977), 69-7310.1090/S0002-9939-1977-0636944-2Search in Google Scholar

[4] S.A. Naimpally and K.L. Singh, Extensions of some fixed point theorems of Rhoades, J. Math. Anal. Appl., 96, (1983), 437-44610.1016/0022-247X(83)90052-5Search in Google Scholar

[5] C.E. Chidume and Ș. Mărușter, Iterative methods for the computation of fixed points of demicontractive mappings, J. Comput. Appl. Math., 234 (3), (2010), 861-882.10.1016/j.cam.2010.01.050Search in Google Scholar

[6] D. Boonchari and S. Saejung, Construction of common fixed points of a count- able family of α -demicontractive mappings in arbitrary Banach spaces, Appl. Math. Comput., 216, (2010), 173-178.10.1016/j.amc.2010.01.027Search in Google Scholar

[7] P.E. Maingé, Regularized and inertial algorithms for common fixed points of non- linear operators, J. Math. Anal. Appl., 344, (2008), 876-887.10.1016/j.jmaa.2008.03.028Search in Google Scholar

[8] M.O. Osilike, Strong and weak convergence of the Ishikawa iteration method for a class of nonlinear equations, Bull. Korean Math. Soc., 37 (1), (2000), 153-169.Search in Google Scholar

[9] M.O. Osilike, Iterative approximation of fixed points of asymptotically demicon- tractive maps, Indian J. Pure Appl. Math., 29 (12), (1998), 1291-1300.Search in Google Scholar

[10] P.E. Maingé and Ș. Mărușter, Convergence in norm of modified Krasnoselski- Mann iterations for fixed points of demicontractive mappings, Appl. Math. Comput., 217 (24), (2011), 9864-9874.10.1016/j.amc.2011.04.068Search in Google Scholar

[11] C.E. Chidume, The solution by iteration of nonlinear equations in certain Banach spaces, J. Nigerian Math. Soc., 3, (1984), 57-62.Search in Google Scholar

[12] A.M. Saddeek, Iterative method for nonlinear pseudo-monotone type operators in Hilbert spaces, Far East J. Appl. Math., 32 (1), (2008), 33-40.Search in Google Scholar

[13] M.O. Osilike and D.I. Igbokwe, Weak and Strong Convergence Theorems for Fixed Points of Pseudocontractions and Solutions of Monotone Type Operator Equa- tions, Comput. Math. Appl., 40, (2000), 559-567.10.1016/S0898-1221(00)00179-6Search in Google Scholar

[14] X. Weng, The iterative solution of nonlinear equations in certain Banach spaces, J. Nigerian Math. Soc., 11, (1992), 1-7.Search in Google Scholar

[15] C.E. Chidume and S.A. Mutangadura, An example on the Mann iteration method for Lipschitz pseudocontractions, Proc. Amer. Math. Soc., 129, (2001), 2359-2363.10.1090/S0002-9939-01-06009-9Search in Google Scholar

[16] A. Genel and J. Lindenstraus, An example concerning fixed points, Israel J. Math., 22 (1), (1975), 81-86.10.1007/BF02757276Search in Google Scholar

[17] L. Mărușter and Ș. Mărușter, Strong convergence of the Mann iteration for α - demicontractive mappings, Math. Comput. Model., 54, (2011), 2486-2492.Search in Google Scholar

[18] K. Nakajo and W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl., 279, (2003), 372-379.10.1016/S0022-247X(02)00458-4Search in Google Scholar

[19] L. Ciric, A. Rafiq, S. Radenovic, M. Racovic and S.U. Ume, On the Mann implicit iteration for strongly accretive and strongly pseudo-contractive mappings, Appl. Math. Comput., 198, (2008), 128-137.10.1016/j.amc.2007.08.027Search in Google Scholar

[20] Rafiq A., On Mann iteration in Hilbert spaces, Nonlinear Anal., 66, (2007), 2230-2236.10.1016/j.na.2006.03.012Search in Google Scholar

[21] M.O. Osilike and F.O. Isiogugu, Fixed points of asymptotically α - demicontractive maps in arbitrary Banach spaces, 15 (3), (2005), 59-67.Search in Google Scholar

[22] H. Zegeye, N. Shahzad and M.A. Alghamdi, Convergence of Ishikawas iteration method for pseudocontractive mappings, Nonlinear Anal., 74, (2011), 7304-7311.10.1016/j.na.2011.07.048Search in Google Scholar

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