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http://dx.doi.org/10.5666/KMJ.2019.59.4.665

An Ishikawa Iteration Scheme for two Nonlinear Mappings in CAT(0) Spaces  

Sokhuma, Kritsana (Department of Mathematics, Faculty of Science and Technology, Phranakhon Rajabhat University)
Publication Information
Kyungpook Mathematical Journal / v.59, no.4, 2019 , pp. 665-678 More about this Journal
Abstract
We construct an iteration scheme involving a hybrid pair of mappings, one a single-valued asymptotically nonexpansive mapping t and the other a multivalued nonexpansive mapping T, in a complete CAT(0) space. In the process, we remove a restricted condition (called the end-point condition) from results of Akkasriworn and Sokhuma [1] and and use this to prove some convergence theorems. The results concur with analogues for Banach spaces from Uddin et al. [16].
Keywords
Ishikawa iteration; CAT(0) spaces; multivalued mapping; asymptotically nonexpansive mapping;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
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1 N. Akkasriworn and K. Sokhuma, Convergence theorems for a pair of asymptotically and multivalued nonexpansive mapping in CAT(0) spaces, Commun. Korean Math. Soc., 30(3)(2015), 177-189.   DOI
2 M. R. Bridson and A. Haeiger, Metric spaces of non-positive curvature, Springer-Verlag, Berlin, 1999.
3 F. Bruhat and J. Tits, Groupes reductifs sur un corps local, Inst. Hautes Etudes Sci. Publ. Math., 41(1972), 5-251.   DOI
4 S. Dhompongsa, W. A. Kirk and B. Panyanak. Nonexpansive set-valued mappings in metric and Banach spaces. J. Nonlinear Convex Anal., 8(2007), 35-45.
5 S. Dhompongsa, W. A. Kirk and B. Sims, Fixed points of uniformly lipschitzian mappings, Nonlinear Anal., 65(2006), 762-772.   DOI
6 W. A. Kirk, Geodesic geometry and fixed point theory, Seminar of Mathematical Analysis(Malaga/Seville, 2002/2003), 195-225, Colecc. Abierta 64, Univ. Sevilla Secr. Publ., Seville, 2003.
7 W. A. Kirk, Geodesic geometry and fixed point theory II, International Conference on Fixed Point Theory and Applications, 113-142, Yokohama Publ., Yokohama, 2004.
8 W. A. Kirk and B. Panyanak, A concept of convergence in geodesic spaces, Nonlinear Anal., 68(2008), 3689-3696.   DOI
9 T. Laokul and B. Panyanak, Approximating fixed points of nonexpansive mappings in CAT(0) spaces, Int. J. Math. Anal., 3 (2009), 1305-1315.
10 W. Laowang and B. Panyanak, A note on common fixed point results in uniformly convex hyperbolic spaces, J. Math., (2013), Art. ID 503731, 5 pp.
11 W. Laowang and B. Panyanak, Approximating fixed points of nonexpansive nonself mappings in CAT(0) spaces, Fixed Point Theory Appl., (2010), Art. ID 367274, 11pp.
12 T. C. Lim, Remarks on some fixed point theorems, Proc. Amer. Math. Soc., 60(1976), 179-182.   DOI
13 B. Nanjaras and B. Panyanak, Demiclosed principle for asymptotically nonexpansive mappings in CAT(0) spaces, Fixed Point Theory Appl., (2010), Art. ID 268780, 14pp.
14 K. Sokhuma, ${\Delta}$-convergence Theorems for a pair of single valued and multivalued nonexpansive mappings in CAT(0) spaces, J. Math. Anal., 4(2013), 23-31.
15 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), Art. ID 618767, 9 pp.
16 I. Uddin, A. A. Abdou and M. Imdad, A new iteration scheme for a hybrid pair of generalized nonexpansive mappings, Fixed Point Theory Appl., (2014), 2014:205, 13pp.
17 I. Uddin and M. Imdad, A new iteration scheme for a hybrid pair of nonexpansive mappings, Honam Math. J., 38(1)(2016), 127-139.   DOI
18 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). 591-600.   DOI