Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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S-ITERATION PROCESS FOR ASYMPTOTIC POINTWISE NONEXPANSIVE MAPPINGS IN COMPLETE HYPERBOLIC METRIC SPACES

  • Received : 2015.10.30
  • Published : 2016.07.31
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Abstract

In this paper, we study the modified S-iteration process for asymptotic pointwise nonexpansive mappings in a uniformly convex hyperbolic metric space. We then prove the convergence of the sequence generated by the modified S-iteration process.

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References

  1. R. P. Agarwal, D. O'Regan, and D. R. Sahu, Iterative construction of fixed point of nearly asymptotically nonexpansive mappings, J. Nonlinear Convex Anal. 8 (2007), no. 1, 61-79.
  2. K. Goebel and W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35 (1972), 171-174. https://doi.org/10.1090/S0002-9939-1972-0298500-3
  3. B. A. Ibn Dehaish, M. A. Khamsi, and A. R. Khan, Mann iteration process for asymptotic pointwise nonexpansive mappings in metric spaces, J. Math. Anal. Appl. 397 (2013), no. 2, 861-868. https://doi.org/10.1016/j.jmaa.2012.08.013
  4. M. A. Khamsi and A. R. Khan, Inequalities in metric spaces with applications, Nonlinear Anal. 74 (2011), no. 12, 4036-4045. https://doi.org/10.1016/j.na.2011.03.034
  5. K. Menger, Untersuchungen uber allgemeine Metrik, Math. Ann. 100 (1928), no. 1, 75-163. https://doi.org/10.1007/BF01448840
  6. S. Reich and I. Shafrir, Nonexpansive iterations in hyperbolic spaces, Nonlinear Anal. 15 (1990), no. 6, 537-558. https://doi.org/10.1016/0362-546X(90)90058-O
  7. J. Schu, Iterative construction of fixed point of asymptotically nonexpansive mapping, J. Math. Anal. Appl. 158 (1991), no. 2, 407-413. https://doi.org/10.1016/0022-247X(91)90245-U