Convergence Theorems for a Hybrid Pair of Nonexpansive Mappings in CAT (0) Spaces

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Kritsana Sokhuma
Apichart Luesamai
Orapun Suwannasen
Pattaraporn Tusto

Abstract

In this paper, we constructed an iteration scheme involving a hybrid pair of the single valued nonexpansive mapping t and the multivalued nonexpansive mapping T of a complete CAT(0) space. In process, we removed a restricted condition (called end-point condition) in Akkasriworn and Sokhuma’s results (Akkasriworn and Sokhuma. 2015: 177–189) and utilized the same to prove some convergence theorems. The result is an expansion from Banach spaces results of Uddin, Abdou and  Imdad. (Uddin, Abdou and  Imdad. 2014: 1–13).

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How to Cite
Sokhuma, K., Luesamai, A., Suwannasen, O., & Tusto, P. (2026). Convergence Theorems for a Hybrid Pair of Nonexpansive Mappings in CAT (0) Spaces. The Golden Teak : Science and Technology Journal (GTSJ.), 6(1), 83–93. retrieved from https://li02.tci-thaijo.org/index.php/gts/article/view/1842
Section
Research Article

References

Akkasriworn, N. & Sokhuma, K. (2015). Convergence theorem for a pair of asymptotically and multivalued nonexpansive mapping. Communications of Korean Mathematical Society, 30(3), 177-189.

Dhompongsa, S., Kirk, W.A. & Panyanak, B. (2007). Nonexpansive set-valued mappings in metric and Banach spaces. Journal of Nonlinear Convex Analysis, 8, 35-45.

Dhompongsa, S., Kirk, W.A. & Sims, B. (2006). Fixed points of uniformly lipschitzian Mappings. Nonlinear Analysis, 65, 762-772.

Ishikawa, S. (1974). Fixed points by a new iteration method. Proceedings of the American Mathematical Society, 44, 147-150.

Kirk, W. A. (2004). Geodesic geometry and fixed point theory II. In International Conference on Fixed Point Theory and Applications (pp.113-142). Yokohama, Japan: Yokohama Publishing.

Kirk, W.A. & Panyanak, B. (2008). A concept of convergence in geodesic spaces. Nonlinear Analysis, 68, 3689-3696.

Laokul, T. & Panyanak, B. (2009). Approximating Fixed Points of Nonexpansive Mappings in CAT(0) Spaces. Int. Journal of Math. Anal, 3, 1305–1315.

Laowang, W. & Panyanak, B. (2010). Approximating fixed points of nonexpansive nonself mappings in CAT(0) spaces. Fixed Point Theory Appl, vol. 2010. Article ID 367274. 11 pages.

Nanjaras, B. & Panyanak, B. (2010). Demiclosed Principle for Asymptotically Nonexpansive Mappings in CAT(0) Space. Fixed Point Theory Appl, vol. 2010. Article ID 268780. 14 pages.

Rhoades, B.E. (1976). Comments on two fixed point iteration methods. Journal. Mathematical Analysis and Application, 56, 741-750.

Sokhuma, K. & Kaewkhao, A. (2010). Ishikawa iterative process for a pair of single-valued and multivalued nonexpansive mappings in Banach spaces. Fixed Point Theory and Applications. DOI : 10.115/2010/618767.

Uddin, I., Abdou, A.A. & Imdad, M. (2014). A new iteration scheme for a hybrid pair of generalized nonexpansive mappings. Fixed Point Theory and Applications, 205, 1-13.

Uddin, I. & Imdad, I. (2016). A new iteration scheme for a hybrid pair of nonexpansive mapping. Honam Mathematical Journal, 38(1), 127-139.

Zhou, H., Agarwal, R.P., Cho, Y.J. & Kim, Y.S. (2002). Nonexpansive mappings and iterative methods in uniformly convex Banach spaces. Georgian Mathematical Journal, 9, 591-600.