Common fixed points of two multivalued nonexpansive mappings by one-step iterative scheme. (English) Zbl 1223.47068

Summary: We introduce a new one-step iterative process to approximate common fixed points of two multivalued nonexpansive mappings in a real uniformly convex Banach space. We establish weak and strong convergence theorems for the proposed process under some basic boundary conditions.


47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H04 Set-valued operators
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[1] Nadler, S. B., Multivalued contraction mappings, Pacific J. Math., 30, 475-488 (1969) · Zbl 0187.45002
[2] Lim, T. C., A fixed point theorem for multivalued nonexpansive mappings in a uniformly convex Banach space, Bull. Amer. Math. Soc., 80, 1123-1126 (1974) · Zbl 0297.47045
[3] Markin, J. T., Continuous dependence of fixed point sets, Proc. Amer. Math. Soc., 38, 545-547 (1973) · Zbl 0278.47036
[4] Gorniewicz, L., Topological Fixed Point Theory of Multivalued Mappings (1999), Kluwer Academic Pub.: Kluwer Academic Pub. Dordrecht, Netherlands · Zbl 0937.55001
[5] Sastry, K. P.R.; Babu, G. V.R., Convergence of Ishikawa iterates for a multivalued mapping with a fixed point, Czechoslovak Math. J., 55, 817-826 (2005) · Zbl 1081.47069
[6] Panyanak, B., Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces, Comp. Math. Appl., 54, 872-877 (2007) · Zbl 1130.47050
[7] Song, Y.; Wang, H., Erratum to “Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces”, Comput. Math. Appl., 55, 2999-3002 (2008) · Zbl 1142.47344
[8] Hu, T.; Huang, J. C.; Rhoades, B. E., A general principle for Ishikawa iterations for multivalued mappings, Indian J. Pure Appl. Math., 28, 8, 1091-1098 (1997) · Zbl 0898.47046
[9] Khan, A. R., On modified Noor iterations for asymptotically nonexpansive mappings, Bull. Belg. Math. Soc. Simon Stevin, 17, 127-140 (2010) · Zbl 1183.47067
[10] Mann, W. R., Mean value methods in iterations, Proc. Amer. Math. Soc., 4, 506-510 (1953) · Zbl 0050.11603
[11] Opial, Z., Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc., 73, 591-597 (1967) · Zbl 0179.19902
[12] Schu, J., Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc., 43, 153-159 (1991) · Zbl 0709.47051
[13] Khan, S. H.; Fukhar-ud-din, H., Weak and strong convergence of a scheme with errors for two nonexpansive mappings, Nonlinear Anal., 8, 1295-1301 (2005) · Zbl 1086.47050
[14] Fukhar-ud-din, H.; Khan, S. H., Convergence of iterates with errors of asymptotically quasi- nonexpansive mappings and applications, J. Math. Anal. Appl., 328, 821-829 (2007) · Zbl 1113.47055
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