Some D-Convergence Theorems in CAT(0) Spaces

Year 2011, Volume: 40 Issue: 4, 563 - 569, 01.04.2011

Mujahid Abbas Safeer Hussain Khan

Keywords

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References

• Bridson, M. and Haefliger, A. Metric Spaces of Non-Positive Curvature (Springer-Verlag, Berlin, Heidelberg, 1999).
• Bruhat, F. and Tits, J. Groupes r´eductifs sur un corps local. I. Donn´ees radicielles valu´ees, Inst. Hautes ´Etudes Sci. Publ. Math. 41, 5–251, 1972.
• Burago, D., Burago, Y. and Ivanov, S. A Course in Metric Geometry, in: Graduate Studies in Math. 33, Amer. Math. Soc., Providence, RI, 2001.
• Das, G. and Debata, J. P. Fixed points of quasi-nonexpansive mappings, Indian J. Pure. Appl. Math. 17, 1263–1269, 1986.
• Dhompongsa, S., Kirk, W. A. and Panyanak, B. Nonexpansive set-valued mappings in metric and Banach spaces, J. Nonlinear Convex Anal. 8, 35–45, 2007.
• Dhompongsa, S., Kirk, W. A. and Sims, B. Fixed points of uniformly lipschitzian mappings, Nonlinear Anal. 65, 762–772, 2006.
• Dhompongsa, S. and Panyanak, B. On △-convergence theorems in CAT(0) spaces, Comput. Math. Appl. 56, 2572–2579, 2008.
• Fukhar-ud-din, H. and Khan, S. H. Convergence of iterates with errors of asymptotically quasi-nonexpansive mappings and applications, J. Math. Anal. Appl. 328, 821–829, 2007. [9] Goebel, K. and Reich, S. Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings (Marcel Dekker, Inc., New York, 1984).
• Gromov, M. Metric structure for Riemannian and non-Riemannian spaces, Progr. Math. 152, Birkhauser, Boston, 1984.
• Kirk, W. A. and Panyanak, B. A concept of convergence in geodesic spaces, Nonlinear Anal. 68, 3689–3696, 2008.
• Khan, S. H. and Fukhar-ud-din, H. Weak and strong convergence of a scheme with errors for two nonexpansive mappings, Nonlinear Anal. 8, 1295–1301, 2005.
• Khan, S. H. and Takahashi, W. Approximating common fixed points of two asymptotically nonexpansive mappings, Sci. Math. Japan 53 (1), 143–148, 2001.
• Lim, T. C. Remarks on some fixed point theorems, Proc. Amer. Math. Soc. 60, 179–182, 1976.
• Reich, S. and Shafrir, I. Nonexpansive iterations in hyperbolic space, Nonlinear Anal. 15, 537–558, 1990.
• Takahashi, W. Iterative methods for approximation of fixed points and their applications, J. Oper. Res. Soc. Japan. 43 (1), 87–108, 2000.
• Takahashi, W. and Tamura, T. Limit theorems of operators by convex combinations of nonexpansive retractions in Banach spaces, J. Approx. Theory 91 (3), 386–397, 1997.