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Approximation of common random fixed point for a finite family of non-self asymtotically nonexpansive random mappings

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In this paper, we study multi-step random iteration scheme with errors for a common random fixed point of a finite family of nonself asymptotically nonexpansive random mappings in real uniformly convex separable Banach spaces. The results presented in this paper extend the recent ones announced by Zhou and Wang [23] and many others.
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581--598
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Bibliogr. 23 poz.
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Bibliografia
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  • [2] I. Beg, M. Abbas, Iterative procedures for solutions of random operator equations in Banach spaces, J. Math. Anal. Appl. 315 (2006), no. 1, 181-201.
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  • [9] S. Itoh, Random fixed point theorems with an application to random differential equations in Banach spaces, J. Math. Anal. Appl. 67 (1979), no. 2, 261-273.
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  • [11] D. O’Regan, A continuation type result for random operators, Proc. Amer. Math. Soc. 126 (1998), 1963-1971.
  • [12] R. Penaloza, A characterization of renegotiation proof contracts via random fixed points in Banach spaces, working paper 269, Department of Economics, University of Brasilia, Brasilia, December 2002.
  • [13] S. Plubtieng, P. Kumam, R. Wangkeeree, Random three-step iteration scheme and common random fixed point of three operators, J. Appl. Math. Stoch. Anal. Vol. 2007, Article ID 82517, 10 pages.
  • [14] S. Plubtieng, K. Ungchittrakool, Weak and strong convergence of finite family with errors of nonexpansive nonself-mappings, Fixed Point Theory and Applications Vol. 2006, Article ID 81493, pages 1-12.
  • [15] J. Schu, Weak and strong convergence theorems to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc. 43 (1991), 153-159.
  • [16] H. F. Senter, W. G. Dotson, Approximating fixed points of nonexpansive mappings, Proc. Amer. Math. Soc. 44 (1974), 375-380.
  • [17] N. Shahzad, Fixed points of set-valued maps, Nonlinear Anal. 45 (2001), 689-692.
  • [18] N. Shahzad, Random fixed points of K-set- and pseudo-contractive random maps, Nonlinear Anal. 57 (2004), 173-181.
  • [19] K. K. Tan, H. K. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl. 178 (1993), 301-308.
  • [20] D. H. Wagner, Survey of measurable selection theorem, SIAM J. Control Optim. 15 (1977), no. 5, 859-903.
  • [21] L. Wang, Some results for nonself asymptotically nonexpansive mappings, Nonlinear Anal. Forum 11 (2006), 23-32.
  • [22] H. K. Xu, I. Beg, Measurability of fixed point sets of multivalued random operators, J. Math. Anal. Appl. 225 (1998), 61-72.
  • [23] X.W. Zhou, L.Wang, Approximation of random fixed points of nonself asymptotically nonexpansive random mappings, Internat. Math. Forum 2 (2007), No. 38, 1859-1868.
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Bibliografia
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bwmeta1.element.baztech-article-PWA5-0025-0012
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