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Số xuất bản: Tập 15 Số 5 (2026): Chuyên san Khoa học Tự nhiên (Tiếng Anh)
Chuyên mục: Khoa học Tự nhiên (Tiếng Anh)
DOI: 10.52714/dthu.ns.3028.1888
Ngày xuất bản: 27/04/2026
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Nguyen, T. H., & Le, T. P. (2026). Convergence of three-step iteration for asymptotically nonexpansive mappings in CAT(0) spaces. Tạp chí Khoa học Đại học Đồng Tháp, 15(5), 103-120. https://doi.org/10.52714/dthu.ns.3028.1888

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Convergence of three-step iteration for asymptotically nonexpansive mappings  in CAT(0) spaces

Nguyen Trung Hieu1, Le Thi Phuong2,
1 Faculty of Mathematics - Informatics Teacher Education, School of Education, Dong Thap University, Cao Lanh 870000, Vietnam
2 Student, Faculty of Mathematics - Informatics Teacher Education, School of Education, Dong Thap University, Cao Lanh 870000, Vietnam

Nội dung chính của bài viết

Tóm tắt

In this paper, we introduce a three-step iteration scheme for approximating common fixed points of three asymptotically nonexpansive mappings in CAT(0) spaces. We also establish and prove some $Delta$-convergence and strong convergence results of this iterative sequence to common fixed points of three asymptotically nonexpansive mappings in complete CAT(0) spaces. In addition, we give an example to illustrate the convergence results obtained.

Từ khóa

asymptotically nonexpansive mapping, three-step iteration scheme, common fixed point, space

Chi tiết bài viết

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Tài liệu tham khảo

Bridson, M., & Haefliger, A. (1999). Metric spaces of non-positive curvature. Springer-Verlag, Berlin, Heidelberg.
Cegielski, A. (2012). Iterative methods for fixed point problems in Hilbert spaces. Lecture Notes in Mathematics 2057. Springer.
Chang, S. S., Wang, L., Lee, H. J., Chan, C. K., & Yang, L. (2012). Demiclosed principle and -convergence theorems for total asymptotically nonexpansive mappings in spaces. Appl. Math. Comput., 219(5), 2611-2617. https://doi.org/10.1016/j.amc.2012.08.095
Dhompongsa, S., & Panyanak, B. (2008). On -convergence theorems in spaces, Comput. Math. Appl., 56(10), 2572-2579. https://doi.org/10.1016/j.camwa.2008.05.036
Dhompongsa, S., Kirk, W. A., & Panyanak, B. (2007). Nonexpansive set-valued mappings in metric and Banach spaces. J. Nonlinear and Convex Anal., 8, 35-45.
Kirk, W. A., & Panyanak, B. (2008). A concept of convergence in geodesic spaces. Nonlinear Anal., 68, 3689-3696. https://doi.org/10.1016/j.na.2007.04.011
Kirk, W. A. (2003). Geodesic geometry and fixed point theory in: seminar of mathematical analysis (Malaga/Seville, 2002/2003), colecc. Abierta, univ. Sevilla secr. Publ. Seville, 64, 195-225.
Kirk, W. A. (2004). Geodesic geometry and fixed point theory II. In International Conference on Fixed Point Theory and Applications, 113-142, Yokohama Publ., Yokohama.
Khan, S. H., & Abbas, M. (2011). Strong and -convergence of some iterative schemes in spaces. Comput. Math. Appl. ,61,109-116. https://doi.org/10.1016/j.camwa.2010.10.037
Lim, T. C. (1976). Remarks on some fixed point theorems. Proc. Amer. Math. Soc., 60, 179–182. https://doi.org/10.1090/S0002-9939-1976-0423139-X
Nanjara, B., & Panyanak, B. (2010). Demiclosedness principle for asymptotically nonexpansive mappings in spaces. Fixed Point Theory Appl., 1-14. https://doi:10.1155/2010/268780
Niwongsa, Y., & Panyanak, B. (2010). Noor iterations for asymptotically nonexpansive mappings in spaces. Int. J. Math. Anal., 4(13), 645-656.
Sahin, A., & Basarir, M. (2013). On the strong convergence of a modified S-iteration process for asymptotically quasi-nonexpansive mapping in space. Fixed Point Theory Appl., 1-10. https://doi:10.1186/1687-1812-2013-12
Sridarat, P., Suparaturatorn, R., Suantai, S., & Cho, Y. J. (2019). Convergence analysis of SP-iteration for -nonexpansive mappings with directed graphs. Bull. Malays. Math. Sci. Soc., 42(5), 2361-2380. https://doi.org/10.1007/s40840-018-0606-0
Sabri, R. I. (2025). A new iteration process for approximate common fixed points for three non-expansive mapping. Iraqi J. Sci., 66(5), 2003-2013. https://doi.org/10.24996/ijs.2025.66.5.19
Tufa, A.R. (2022). New iterative methods for finding common fixed points of two non-self mappings in a real Hilbert space. Topol. Algebra Appl., 10(1), 36-46. https://doi.org/10.1515/taa-2022-0111
Tufa, A.R. (2023). A new iterative method for approximating common fixed points of two non-self mappings in a CAT(0) space. Rend. Circ. Mat. Palermo, 72, 4053-4065. https://doi.org/10.1007/s12215-023-00885-5
Yambangwai, D., & Thianwan, T. (2021). ∆-Convergence and strong convergence for asymptotically nonexpansive mappings on a space. Thai J. Math., 19(3), 813-826.
Yambangwai, D., Aunruean, S., & Thianwan, T. (2020). A new modified three-step iteration method for -nonexpansive mappings in Banach spaces with a graph. Numerical Algorithms, 84(2), 537-565. https://doi.org/10.1007/s11075-019-00768-w
Zhou, H., Agarwal, R. P., Cho, Y. J., & Kim, Y. S. (2002). Nonexpansive mappings and iterative methods in uniformly convex Banach spaces. Georgian Math. J. 9, 591-600. https://doi.org/10.1515/GMJ.2002.591

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