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Convergence of three-step iterations for Ciric-quasi contractive operator in CAT(0) spaces


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[1] M. Abbas, T. Nazir, A new faster iteration process applied to constrained minimization feasibility problems, Mat. Vesnik, 66 (2) (2014), 223-234Search in Google Scholar

[2] R. P. Agarwal, Donal O’Regan and D.R. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, Nonlinear Convex Anal., 8 (1) (2007), 61-79.Search in Google Scholar

[3] A. Abkar, M. Eslamian, Common fixed point results in CAT(0) spaces, Nonlinear Anal.: TMA, 74 (5) (2011), 1835-1840.10.1016/j.na.2010.10.056Search in Google Scholar

[4] V. Berinde, Iterative approximation of fixed points, Baia Mare: Efemeride, 2000.Search in Google Scholar

[5] V. Berinde, Picard iteration converges faster than Mann iteration for a class of quasi contractive operators, Fixed Point Theory Appl., 2 (2004), 97-105.10.1155/S1687182004311058Search in Google Scholar

[6] V. Berinde, Iterative approximation of fixed points, Springer-Verlag, Berlin Heidelberg, 2007.10.1109/SYNASC.2007.49Search in Google Scholar

[7] A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., 29 (2002), 531-536.10.1155/S0161171202007524Search in Google Scholar

[8] M. R. Bridson, A. Haefliger, 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

[9] F. Bruhat, J. Tits, ”Groups reductifs sur un corps local”, Institut des Hautes Etudes Scientifiques. Publications Mathematiques, 41 (1972), 5-251.10.1007/BF02715544Search in Google Scholar

[10] L. B. Ciric, A generalization of Banach principle, Proc. Amer. Math. Soc., 45 (1974), 727-730.Search in Google Scholar

[11] P. Chaoha and A. Phon-on, A note on fixed point sets in CAT(0) spaces, J. Math. Anal. Appl., 320 (2) (2006), 983-987.10.1016/j.jmaa.2005.08.006Search in Google Scholar

[12] S. K. Chatterjae, Fixed point theorems compactes, Rend. Acad. Bulgare Sci., 25 (1972), 727-730.Search in Google Scholar

[13] S. Dhompongsa, A. Kaewkho, B. Panyanak, Lim’s theorems for multivalued mappings in CAT(0) spaces, J. Math. Anal. Appl., 312 (2) (2005), 478-487.10.1016/j.jmaa.2005.03.055Search in Google Scholar

[14] S. Dhompongsa, B. Panyanak, On Δ-convergence theorem in CAT(0) spaces, Comput. Math. Appl., 56 (10) (2008), 2572-2579.10.1016/j.camwa.2008.05.036Search in Google Scholar

[15] R. Espinola, A. Fernandez-Leon, CAT(k)-spaces, weak convergence and fixed point, J. Math. Anal. Appl., 353 (1) (2009), 410-427.10.1016/j.jmaa.2008.12.015Search in Google Scholar

[16] N. Hussain, M.A. Khamsi, On asymptotic pointwise contractions in metric spaces, Nonlinear Anal.: TMA 71, (10) (2009), 4423-4429.10.1016/j.na.2009.02.126Search in Google Scholar

[17] S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc., 44 (1974), 147-150.10.1090/S0002-9939-1974-0336469-5Search in Google Scholar

[18] R. Kannan, Some results on fixed point theorems, Bull. Calcutta Math. Soc., 60 (1969), 71-78.Search in Google Scholar

[19] M. A. Khamsi, W. A. Kirk, An introduction to metric spaces and fixed point theory, Pure Appl. Math, Wiley-Interscience, New York, NY, USA, 2001.10.1002/9781118033074Search in Google Scholar

[20] S. H. Khan, M. Abbas, Strong and _-convergence of some iterative schemes in CAT(0) spaces, Comput. Math. Appl., 61 (1) (2011), 109-116.10.1016/j.camwa.2010.10.037Search in Google Scholar

[21] A. R. Khan, M. A. Khamsi, H. Fukhar-ud-din, Strong convergence of a general iteration scheme in CAT(0) spaces, Nonlinear Anal.: TMA, 74 (3) (2011), 783-791. 10.1016/j.na.2010.09.029Search in Google Scholar

[22] W. A. Kirk, Geodesic geometry and fixed point theory, in Seminar of Mathematical Analysis (Malaga/Seville, 2002/2003), Vol. 64 of Coleccion Abierta, 195-225, University of Seville Secretary of Publications, Seville, Spain, 2003.Search in Google Scholar

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

[24] W. Laowang, B. Panyanak, Strong and Δ convergence theorems for multivalued mappings in CAT(0) spaces, J. Inequal. Appl., Vol. 2009, Article ID 730132, 16 pages, 2009.Search in Google Scholar

[25] L. Leustean, A quadratic rate of asymptotic regularity for CAT(0)-spaces, J. Math. Anal. Appl., 325 (1) (2007), 386-399.10.1016/j.jmaa.2006.01.081Search in Google Scholar

[26] W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc., 4 (1953), 506-510.10.1090/S0002-9939-1953-0054846-3Search in Google Scholar

[27] Y. Niwongsa, B. Panyanak, Noor iterations for asymptotically nonexpansive mappings in CAT(0) spaces, Int. J. Math. Anal., 4 (13) (2010), 645-656.10.1155/2010/268780Search in Google Scholar

[28] M. A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl., 251 (1) (2000), 217-229.10.1006/jmaa.2000.7042Search in Google Scholar

[29] A. Rafiq, Fixed points of Ciric quasi-contractive operators in generalized convex metric spaces, General Math., 14 (3) (2006), 79-90.Search in Google Scholar

[30] B. E. Rhoades, Fixed point iteration using infinite matrices, Trans. Amer. Math. Soc., 196 (1974), 161-176.10.1090/S0002-9947-1974-0348565-1Search in Google Scholar

[31] S. Saejung, Halpern’s iteration in CAT(0) spaces, Fixed Point Theory Appl., Vol. 2010, Article ID 471781, 13 pages, 2010.Search in Google Scholar

[32] N. Shahzad, Fixed point results for multimaps in CAT(0) spaces, Topology and its Applications, 156 (5) (2009), 997-1001.10.1016/j.topol.2008.11.016Search in Google Scholar

[33] D. Thakur, B. S. Thakur, M. Postolache, New iteration scheme for numerical reckoning fixed points of nonexpansive mappings, J. Ineq. Appl., 2014:328, 2014.10.1186/1029-242X-2014-328Search in Google Scholar

[34] T. Zamfirescu, Fixed point theorems in metric space, Arch. Math. (Basel), 23 (1972), 292-298. 10.1007/BF01304884Search in Google Scholar

eISSN:
2066-7752
Język:
Angielski
Częstotliwość wydawania:
2 razy w roku
Dziedziny czasopisma:
Mathematics, General Mathematics