Strong convergence of a modified SP-iteration process for generalized asymptotically quasi- nonexpansive mappings in CAT(0) spaces

Volume 9, Issue 5, pp 2126--2135 http://dx.doi.org/10.22436/jnsa.009.05.18

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Authors

Duangkamon Kitkuan - Department of Mathematics, Faculty of Science and Technology, Rambhai Barni Rajabhat University (RBRU), 41 M.5 Sukhumvit Road, Thachang, Mueang, Chanthaburi 22000, Thailand. Anantachai Padcharoen - Department of Mathematics, Faculty of Science and Technology, Rambhai Barni Rajabhat University (RBRU), 41 M.5 Sukhumvit Road, Thachang, Mueang, Chanthaburi 22000, Thailand.

Abstract

In this paper, we establish strong convergence theorems of the modified SP-iteration generalized asymptotically quasi-nonexpansive mapping in CAT(0) spaces which extend and improve the recent ones announced by Phuengrattana and Suantai [W. Phuengrattana, S. Suantai, J. Comput. Appl. Math., 235 (2011), 3006- 3014], Sahin and Basarir [A. Sahin, M. Basarir, J. Inequal. Appl., 2013 (2013), 10 pages], Nanjaras and Panyanak [B. Nanjaras, B. Panyanak, Fixed Point Theory Appl., 2010 (2010), 14 pages] and some others.

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Keywords

• Generalized asymptotically quasi-nonexpansive mapping
• SP-iteration
• CAT(0) space.

MSC

•  47H09
•  47H10

References

• [1] M. R. Bridson, A. Hae iger, Metric Spaces of Non-positive Curvature, Springer-Verlag, Berlin (1999)


• [2] F. Bruhat, J. Tits, Groupes reductifs sur un corps local, Inst. Hautes Étude Sci. Publ. Math., 41 (1972), 5-251.


• [3] S. Dhompongsa, A. Kaewkhao, B. Panyanak, Lim's theorems for multivalued mappings in CAT(0) spaces, J. Math. Anal. Appl., 312 (2005), 478-487.


• [4] S. Dhompongsa, W. A. Kirk, B. Panyanak, Nonexpansive set-valued mappings in metric and Banach spaces, J. Nonlinear Convex Anal., 8 (2007), 35-45.


• [5] S. Dhompongsa, B. Panyanak , On \(\Delta\) -convergence theorem in CAT(0) spaces, Comput. Math. Appl., 56 (2008), 2572-2579.


• [6] H. Fukhar-ud-din, A. A. Domlo, A. R. Khan, Strong convergence of an implicit algorithm in CAT(0) spaces, Fixed Point Theory Appl., 2011 (2011), 11 pages.


• [7] K. Goebel, W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35 (1972), 171-174.


• [8] S. H. Khan, M. Abbas, Strong and \(\Delta\) -convergence of some iterative schemes in CAT(0) spaces , Comput. Math. Appl., 61 (2011), 109-116.


• [9] W. A. Kirk, Geodesic geometry and fixed point theory, In: Seminar of Math. Anal., Malaga/Seville, Colecc. Abierta, Univ. Seville Secr. Publ., Seville, 64 (2003), 195-225.


• [10] W. A. Kirk, Fixed point theory in CAT(0) spaces and R-trees, Fixed Point Theory Appl., 4 (2004), 309-316.


• [11] W. A. Kirk, Geodesic geometry and fixed point theory II, In: International Conference on Fixed Point Theory Appl., Yokohama Publ., Yokohama, (2004), 113-142.


• [12] W. A. Kirk, B. Panyanak, A concept of convergence in geodesic spaces, Nonlinear Anal., 68 (2008), 3689-3696.


• [13] P. Kumam, G. S. Saluja, H. K. Nashine, Convergence of modified S-iteration process for two asymptotically nonexpansive mappings in the intermediate sense in CAT(0) spaces, J. Inequalities Appl., 2014 (2014), 15 pages.


• [14] T. C. Lim , Remarks on some fixed point theorems, Proc. Am. Math. Soc., 60 (1976), 179-182.


• [15] B. Nanjaras, B. Panyanak, Demiclosed principle for asymptotically nonexpansive mappings in CAT(0) spaces, Fixed Point Theory Appl., 2010 (2010), 14 pages.


• [16] W. Phuengrattana, S. Suantai, On the rate of convergence of Mann, Ishikawa, Noor and SP-iterations for continuous functions on an arbitrary interval, J. Comput. Appl. Math., 235 (2011), 3006-3014.


• [17] A. Sahin, M. Basarir , On the strong and \(\Delta\) -convergence of SP-iteration on CAT(0) space, J. Inequal. Appl., 2013 (2013), 10 pages.


• [18] P. Saipara, P. Chaipunya, Y. J. Cho, P. Kumam , On strong and \(\Delta\) -convergence of modified S-iteration for uniformly continuous total asymptotically nonexpansive mappings in CAT(\(\kappa\)) spaces , J. Nonlinear Sci. Appl., 8 (2015), 965-975.


• [19] J. F. Tang, S. S. Chang, H. W. Joseph Lee, C. K. Chan, Iterative Algorithm and \(\Delta\)-convergence theorems for total asymptotically nonexpansive mappings in CAT(0) spaces, Abstr. Appl. Anal., 2012 (2012), 11 pages.


• [20] L. Wang, S. S. Chang, Z. Ma, Convergence theorems for total asymptotically nonexpansive non-self mappings in CAT(0) Spaces , J. Inequalities Appl., 2013 (2013), 10 pages.


• [21] H. Y. Zhou, Y. J. Cho, M. Grabiec, Iterative process for generalized asymptotically nonexpansive mapping in Banach spaces, Panamer. Math. J., 13 (2003), 99-107.


• [22] H. Y. Zhou, G. L. Gao, G. T. Guo, Y. J. Cho, Some general convergence principles with application, Bull. Korean Math. Soc., 40 (2003), 351-363.