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On the convergence of an iterative method for asymptotically nonexpansive mappings in intermediate sense

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Języki publikacji
EN
Abstrakty
EN
In this paper, we introduced an iterative method for approximating a fixed point of asymptotically non-expansive mappings in the intermediate sense in a uniformly convex Banach space. We establish some strong and weak convergence theorems.
Rocznik
Tom
Strony
43--60
Opis fizyczny
Bibliogr. 26 poz.
Twórcy
autor
  • Department of Mathematics Nri Institute of Information Science & Technology Bhopal, 462021, India
autor
  • Department of Mathematics J H Government Postgraduate College, Betul, 460001, India
Bibliografia
  • [1] Bruck R., Kuczumow T., Reich S., Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property, Colloq. Math., 65(2)(1993), 169-179.
  • [2] Cho Y.J., Zhou H.Y., Guo G., Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings, Comput. Math. Appl., 47(4-5)(2004), 707-717.
  • [3] Glowinski R., Le Tallec P., Augmented Lagrangian and operator-splitting methods in nonlinear mechanics, SIAM Studies in Applied Mathematics, 9. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1989.
  • [4] Goebel K., Kirk W.A., A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35(1972), 171-174.
  • [5] Haubruge S., Nguyen V.H., Strodiot J.J., Convergence analysis and applications of the Glowinski-Le Tallec splitting method for finding a zero of sum of two maximal monotone operators, J. Optim. Theory Appl., 97(3)(1998), 645-673.
  • [6] Hicks T., Kubicek J., On the Mann iteration process in a Hilbert space, J. Math. Anal. Appl., 59(3)(1977), 498-504.
  • [7] Ishikawa S., Fixed points by a new iteration, Proc. Amer. Math. Soc., 44(1974), 147-150.
  • [8] Kim G.E., Kim T.H., Mann and Ishikawa iterations with errors for non- Lipschitzian mappings in Banach spaces, Comput. Math. Appl., 42(12)(2001), 1565-1570.
  • [9] Kirk W.A., Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive type, Israel J. Math., 17(1974), 339-346.
  • [10] Mann W.R., Mean value methods in iteration, Proc. Amer. Math. Soc., 4(1953), 506-510.
  • [11] Nammanee K., Noor M.A., Suantai S., Convergence criteria of modified Noor iterations with errors for asymptotically nonexpansive mappings, J. Math. Anal. Appl., 314(1)(2006), 320-334.
  • [12] Nammanee K., Suantai S., The modified Noor iterations with errors for non-Lipschitzian mappings in Banach spaces, Applied Mathematics and Computation, l87(2007), 669-679.
  • [13] Nilsrakoo W., Saejung S., A reconsideration on convergence of three-step iterations for asymptotically nonexpansive mappings, Appl. Math. Comput., l90(2007), l472-l478.
  • [14] Aslam Noor M., New approximation schemes for general variational inequalities, J. Math. Anal. Appl., 25l(l)(2000), 2l7-229.
  • [15] Aslam Noor M., Three-step iterative algorithms for multivalued quasi variational inclusions, J. Math. Anal. Appl., 255(2)(200l), 589-604.
  • [16] Opial Z., Weak convergence of the sequence of successive approximation for nonexpansive mappings, Bull. Amer. Math. Soc., 73(l967), 59l-597.
  • [17] Plubtieng S., Wangkeeree R., Strong convergence for multi-step Noor iterations with errors in Banach spaces, J. Math. Anal. Appl., 32l(l)(2006), l0-23.
  • [18] Rhoades B.E., Fixed point iterations for certain nonlinear mappings, J. Math. Anal. Appl., l83(l)(l994), ll8-l20.
  • [19] Schu J., Iterative construction of fixed points of asymptotically nonexpansive mappings, J. Math. Anal. Appl., l58(3)(l99l), 407-4l3.
  • [20] Schu J., Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc., 43(l)(l99l), l53-l59.
  • [21]Senter H.F., Dotson W.G.Jr., Approximating fixed points of nonexpansive mappings, Proc. Amer. Math. Soc., 44(l974), 375-380.
  • [22] Suantai S., Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings, J. Math. Anal. Appl., 3ll(2)(2005), 506-5l7.
  • [23] Tan K.K., Xu H.K., Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl., l78(2)(l993), 30l-308.
  • [24] Xu H.K., Inequalities in Banach spaces with applications, Nonlinear Anal., l6(l2)(l99l), ll27-ll38.
  • [25] Xu H.K., Existence and convergence for fixed points of mappings of asymp¬totically nonexpansive type, Nonlinear Anal., l6(l2)(l99l), ll39-ll46.
  • [26] Xu B.L., Noor M.A., Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., 267(2)(2002), 444-453.
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Bibliografia
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