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The modified Ishikawa iteration process with errors in CAT(0) spaces

   | 28 dic 2020
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[1] Bridson, M. and Haefliger, A., Metric Spaces of Non-Positive Curvature, vol. 319 of Grundlehren der Mathematischen Wissenschaften, Springer, Berlin, Germany, 1999.10.1007/978-3-662-12494-9Search in Google Scholar

[2] Brown, K.S., Buildings, Springer, New York, NY, USA, 1989.Search in Google Scholar

[3] Bruck, R.E., Kuczumow, T. and Reich, S., Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property, Colloqium Math. LXV. 169-179 (1993)10.4064/cm-65-2-169-179Search in Google Scholar

[4] Dhompongsa, S., Kirk, W.A. and Panyanak, B., Nonexpansive set-valued mappings in metric and Banach spaces, J. Nonlinear Convex Anal. 8(1) (2007), pp. 35-45.Search in Google Scholar

[5] Dhompongsa, S., Kirk, W.A. and Sims, B., Fixed points of uniformly Lip-schitzian mappings, Nonlinear Anal. Theory Methods Appl. 65(4) (2006), pp. 762-772.10.1016/j.na.2005.09.044Search in Google Scholar

[6] Dhompongsa, S. and Payanak, B., On Δ-convergence theorems in CAT(0) spaces, Comput. Math. Appl. 56 (2008), pp. 2572-2579.10.1016/j.camwa.2008.05.036Search in Google Scholar

[7] Geobel, K. and Kirk, W.A., A fixed point theorem for asymptotically non-expansive mappings, Proc. Amer. Math. Soc. 35 (1972), pp. 171-174.10.1090/S0002-9939-1972-0298500-3Search in Google Scholar

[8] Goebel, K. and Reich, S., Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings, Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 83 (1984).Search in Google Scholar

[9] Hussain, N. and Khamsi, M.A., On asymptotic pointwise contractions in metric spaces, Nonlinear Anal. 71 (2009), pp. 4423-4429.10.1016/j.na.2009.02.126Search in Google Scholar

[10] Kirk, W.A., Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive types, Israel J. Math. 17 (1974), pp. 339-346.10.1007/BF02757136Search in Google Scholar

[11] Kirk, W.A., Fixed point theorems in CAT(0) spaces and 𝕉-trees, Fixed Point Theory Appl., vol. 4 (2004), pp. 309-316.Search in Google Scholar

[12] Kirk, W.A., Geodesic geometry and fixed point theory. II, in International Conference on Fixed Point Theory and Applications, pp. 113-142, Yokohama Publ., 2004.10.1155/S1687182004406081Search in Google Scholar

[13] Kirk, W.A., Geodesic geometry and fixed point theory, in Seminar of Mathematical Analysis (Malaga/Seville, 2002/2003), vol. 64 of Colecc. Abierta, pp.195-225, Universidad de Sevilla Secr. Publ., Seville, Spain, 2003.Search in Google Scholar

[14] Kirk, W.A. and Panyanak, B., A concept of convergence in geodesic spaces, Nonlinear Anal. Theory Methods Appl. 68 (2006), pp. 3689-3696.10.1016/j.na.2007.04.011Search in Google Scholar

[15] Kaczor, W. and Walczuk, J., A mean ergodic theorem for mappings which are asymptotically nonexpansive in the intermediate sense, Nonlinear Anal. Theory Methods Appl. 47 (2001), pp. 2731-2742.10.1016/S0362-546X(01)00392-3Search in Google Scholar

[16] Lim, T.C., Remarks on some fixed point theorems, Proc. Amer. Math. Soc. 60 (1976), pp. 179-182.10.1090/S0002-9939-1976-0423139-XSearch in Google Scholar

[17] Nanjaras, B. and Panyanak, B., Demiclosed principle for asymptotically nonexpansive mappings in CAT(0) spaces, Fixed Point Theory Appl. (2010). (Article ID 268780)10.1155/2010/268780Search in Google Scholar

[18] Osilike., M.O. and Aniagbosor, SC., Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings, Math. Comput. Modelling, 32 (2000), pp. 1181-1191.10.1016/S0895-7177(00)00199-0Search in Google Scholar

[19] Panyanak, P. and Loakul. T., On the Ishikawa iteration process in CAT(0) spaces, Bull. Iranian Math. Soc., 37 (2011), pp. 185-197.Search in Google Scholar

[20] Rhoades, B.E. and Soltuz, S.M., The equivalence between the convergences of Ishikawa and Mann iterations for an asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive maps, J. Math. Anal. Appl. 289 (2004), pp. 266-278.10.1016/j.jmaa.2003.09.057Search in Google Scholar

[21] Schu, j., Weak and strong convergence to fixed of asymptotically nonexpansive mappings, Bull. Australian Math. Soc. 43 (1991), pp. 153-159.10.1017/S0004972700028884Search in Google Scholar

[22] Tan, K.K. and Xu, H.K., Fixed point iteration processes for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 122 (2011), pp. 733-739.10.1090/S0002-9939-1994-1203993-5Search in Google Scholar

[23] Xu, H.K., Existence and convergence for fixed points of mappings of asymptotically nonexpansive type, Nonlinear Anal. Theory Methods Appl. 16 (1991), pp. 1139-1146.10.1016/0362-546X(91)90201-BSearch in Google Scholar

[24] Zhang, J. and Cui, Y., Existence and convergence of fixed points for mappings of asymptotically nonexpansive type in uniformly convex W-hyperbolic spaces, Fixed Point Theory Appl. (2011).10.1186/1687-1812-2011-39Search in Google Scholar

eISSN:
1844-0835
Lingua:
Inglese
Frequenza di pubblicazione:
Volume Open
Argomenti della rivista:
Mathematics, General Mathematics