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Three-step iterations for variational inequalities and nonexpansive mappings. (English) Zbl 1128.65051
The authors propose a new three-step iterative method for finding the common elements of the variational inequalities and the fixed points of the nonexpansive mappings. They also consider the convergence analysis of the new method for the strongly inverse co-coercive mappings. The results proved in this paper may be viewed as an important improvement of the previously known results. They are to some extent general in nature and may stimulate the topic of research.

MSC:
65K10 Numerical optimization and variational techniques
49J40 Variational inequalities
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[1] Bnouhachem, A.; Noor, M. Aslam; Rassias, Th. M., Three-steps iterative algorithms for mixed variational inequalities, Appl. math. comput., 183, 436-446, (2006) · Zbl 1111.65058
[2] Browder, F.E.; Petryshyn, W.V., Construction of fixed points of nonlinear mappings in Hilbert spaces, J. math. anal. appl., 20, 197-228, (1967) · Zbl 0153.45701
[3] Liu, F.; Nashed, M.Z., Regularization of nonlinear ill-posed variational inequalities and convergence rates, Set-valued anal., 6, 313-344, (1998) · Zbl 0924.49009
[4] Takahashi, W., Nonlinear functional analysis, (2000), Yokohama Publishers Yokohama, Japan
[5] Takahashi, W.; Toyoda, M., Weak convergence theorems for nonexpansive mappings and monotone mappings, J. optim. theory appl., 118, 417-428, (2003) · Zbl 1055.47052
[6] Noor, M. Aslam, Some algorithms for general monotone variational inequalities, Math. comput. model., 29, 1-9, (1999) · Zbl 0991.49004
[7] Noor, M. Aslam, New approximation schemes for general variational inequalities, J. math. anal. appl., 251, 217-229, (2000) · Zbl 0964.49007
[8] Noor, M. Aslam, Some developments in general variational inequalities, Appl. math. comput., 191-277, (2004) · Zbl 1134.49304
[9] M. Aslam Noor, General variational inequalities and nonexpansive mappings, J. Math. Anal. Appl., in press, doi:10.1016/j.jmaa.2006.09.039. · Zbl 1112.49013
[10] M. Aslam Noor, Z. Huang, Three-step methods for nonexpansive mappings and variational inequalities, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.08.088. · Zbl 1128.65050
[11] Noor, M. Aslam; Bnouhachem, A., On an iterative algorithm for general variational inequalities, Appl. math. comput., 185, 155-168, (2007) · Zbl 1119.65058
[12] Osilike, M.O., Weak and strong convergence theorems for fixed points of pseudocontractions and solutions of monotone type operator equations, Comput. math. appl., 40, 559-567, (2000) · Zbl 0958.47030
[13] Suzuki, T., Strong convergence of Krasnoselskii and mann’s type sequences for one-parameter nonexpansive semigroups without Bochner integrals, J. math. anal. appl., 305, 227-239, (2005) · Zbl 1068.47085
[14] Xu, H.K., Viscosity approximation methods for nonexpansive mappings, J. math. anal. appl., 298, 279-291, (2004) · Zbl 1061.47060
[15] Y. Yao, J.C. Yao, On modified iterative method for nonexpansive mappings and monotone mappings, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.08.062. · Zbl 1121.65064
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