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Convergence of modified s-iteration process for two asymptotically quasi-nonexpansive type mappings in CAT(0) spaces

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EN
Abstrakty
EN
The purpose of this paper is to study convergence of a newly defined modified S-iteration process to a common fixed point of two asymptotically quasi-nonexpansive type mappings in the setting of CAT(0) space. We give a sufficient condition for convergence to a common fixed point and establish some strong convergence theorems for the said iteration process and mappings under suitable conditions. Our results extend and improve many known results from the existing literature.
Wydawca
Rocznik
Strony
107--118
Opis fizyczny
Bibliogr. 25 poz.
Twórcy
autor
  • Department f Mathematics Govt. Nagarjuna P.G. College of Science, Raipur - 492010 (C.G.), India
Bibliografia
  • [1] R. P. Agarwal, D. O’Regan, D. R. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J. Nonlinear Convex Anal. 8(1) (2007), 61–79.
  • [2] M. R. Bridson, A. Haefliger, Metric Spaces of Non-Positive Curvature, Vol. 319 of Grundlehren der Mathematischen Wissenschaften, Springer, Berlin, Germany, 1999.
  • [3] K. S. Brown, Buildings, Springer, New York, NY, USA, 1989.
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  • [5] J. B. Diaz, F. T. Metcalf, On the structure of the set of subsequential limit points of successive approximations, Bull. Amer. Math. Soc. 73 (1967), 516–519.
  • [6] H. Fukhar-ud-din, S. H. Khan, Convergence of iterates with errors of asymptotically quasi-nonexpansive and applications, J. Math. Anal. Appl. 328 (2007), 821–829.
  • [7] K. Goebel, W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35 (1972), 171–174.
  • [8] K. Goebel, S. Reich, Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings, Vol. 83 of Monograph and Textbooks in Pure and Applied Mathematics, Marcel Dekker Inc., New York, NY, USA, 1984.
  • [9] M. A. Khamsi, W. A. Kirk, An Introduction to Metric Spaces and Fixed Point Theory, Pure and Applied Mathematics, Wiley-Interscience, New York, NY, USA, 2001.
  • [10] S. H. Khan, M. Abbas, Strong and Δ-convergence of some iterative schemes in CAT(0) spaces, Comput. Math. Appl. 61(1) (2011), 109–116.
  • [11] A. R. Khan, M. A. Khamsi, H. Fukhar-ud-din, Strong convergence of a general iteration scheme in CAT(0) spaces, Nonlinear Anal. 74(3) (2011), 783–791.
  • [12] W. A. Kirk, Fixed point theory in CAT(0) spaces and R-trees, Fixed Point Theory Appl. 4 (2004), 309–316.
  • [13] W. A. Kirk, Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive type, Israel J. Math. 17 (1974), 339–346.
  • [14] 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.
  • [15] 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.
  • [16] Q. H. Liu, Iterative sequences for asymptotically quasi-nonexpansive mappings, J. Math. Anal. Appl. 259 (2001), 1–7.
  • [17] Q. H. Liu, Iterative sequences for asymptotically quasi-nonexpansive mappings with error member, J. Math. Anal. Appl. 259 (2001), 18–24.
  • [18] Y. Niwongsa, B. Panyanak, Noor iterations for asymptotically nonexpansive mappings in CAT(0) spaces, Int. J. Math. Anal. 4(13) (2010), 645–656.
  • [19] D. R. Sahu, J. S. Jung, Fixed point iteration processes for non-Lipschitzian mappings of asymptotically quasi-nonexpansive type, Int. J. Math. Math. Sci. 33 (2003), 2075–2081.
  • [20] A. Şahin, M. Başarir, On the strong convergrnce of a modified S-iteration process for asymptotically quasi-nonexpansive mapping in CAT(0) space, Fixed Point Theory Appl. 2013, 2013:12.
  • [21] G. S. Saluja, Strong convergence theorem for two asymptotically quasi-nonexpansive mappings with errors in Banach space, Tamkang J. Math. 38(1) (2007), 85–92.
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  • [23] N. Shahzad, A. Udomene, Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces, Fixed Point Theory Appl., Vol. 2006, Article ID 18909, Pages 1-10.
  • [24] 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.
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Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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