Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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CONVERGENCE THEOREMS FOR A PAIR OF ASYMPTOTICALLY AND MULTIVALUED NONEXPANSIVE MAPPING IN CAT(0) SPACES

  • AKKASRIWORN, NAKNIMIT (Department of Mathematics Faculty of Science and Technology Rambhai Barni Rajabhat University) ;
  • SOKHUMA, KRITSANA (Department of Mathematics Faculty of Science and Technology Muban Chom Bueng Rajabhat University)
  • Received : 2014.11.21
  • Published : 2015.06.30
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Abstract

In this paper, we prove ${\Delta}$-convergence theorems for Ishikawa iteration of asymptotically and multivalued nonexpansive mapping in CAT(0) spaces. This results we obtain are analogs of Banach spaces results of Sokhuma [13].

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References

  1. M. Bridson and A. Haefliger, Metric Spaces of Non-Positive Curvature, Springer, Berlin 1999.
  2. F. Bruhat and J. Tits, Groupes reductifs sur un corps local I. Donnees radicielles valuees, Inst. Hautes Etudes Sci. Publ. Math. 41 (1972), 5-251. https://doi.org/10.1007/BF02715544
  3. S. Dhompongsa, W. A. Kirk, and B. Panyanak, Nonexpansive set-valued mappings in metric and Banach spaces, J. Nonlinear Convex Anal. 8 (2007), no. 1, 35-45.
  4. S. Dhompongsa, W. A. Kirk, and B. Sims, Fixed points of uniformly lipschitzian mappings, Nonlinear Anal. 65 (2006), no. 4, 762-772. https://doi.org/10.1016/j.na.2005.09.044
  5. J. Garcia-Falset, E. L. Fuster, and S. Prus, The fixed point property for mappings admitting a center, Nonlinear Anal. 66 (2007), no. 6, 1257-1274. https://doi.org/10.1016/j.na.2006.01.016
  6. W. A. Kirk, Geodesic geometry and fixed point theory II, International Conference on Fixed Point Theory and Applications, 113-142, Yokohama Publishers, Yokohama, Japan, 2004.
  7. W. A. Kirk and B. Panyanak, A concept of convergence in geodesic spaces, Nonlinear Anal. 68 (2008), no. 12, 3689-3696. https://doi.org/10.1016/j.na.2007.04.011
  8. T. Laokul and B. Panyanak, Approximating fixed points of nonexpansive mappings in CAT(0) spaces, Int. J. Math. Anal. 3 (2009), no. 25-28, 1305-1315.
  9. W. Laowang and B. Panyanak, Approximating fixed points of nonexpansive nonself mappings in CAT(0) spaces, Fixed Point Theory Appl. 2010 (2010), Article ID 367274, 11 pages.
  10. W. Laowang and B. Panyanak, A note on common fixed point results in uniformly convex hyperbolic spaces, J. Math. 2013 (2013), Article ID 503731, 5 pages.
  11. T. C. Lim, Remarks on some fixed point theorems, Proc. Amer. Math. Soc. 60 (1976), 179-182. https://doi.org/10.1090/S0002-9939-1976-0423139-X
  12. B. Nanjaras and B. Panyanak, Demiclosed principle for asymptotically nonexpansive mappings in CAT(0) spaces, Fixed Point Theory Appl. 2010 (2010), Article ID 268780, 14 pages.
  13. K. Sokhuma, ${\Delta}$-convergence theorems for a pair of single-valued and multivalued nonexpansive mappings in CAT(0) spaces, J. Math. Anal. 4 (2013), no. 2, 23-31.
  14. K. Sokhuma and A. Kaewkhao, Ishikawa iterative process for a pair of single-valued and multivalued nonexpansive mappings in Banach spaces, Fixed Point Theory Appl. 2010 (2010), Article ID 618767, 9 pages.
  15. H. Zhou, R. P. Agarwal, Y. J. Cho, and Y. S. Kim, Nonexpansive mappings and iterative methods in uniformly convex Banach spaces, Georgian Math. J. 9 (2002), no. 3, 591-600.

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