Convergence of mann iteration process to a fixed point of (α,β) - nonexpansive mappings in Lp spaces
Main Article Content
Abstract
In this paper, we prove the convergence of Mann iteration to fixed points of (α,β) -nonexpansive and strictly pseudo-contractive mappings in spaces. In addition, by using the obtained results, we state the convergence of Mann iteration to solutions of the nonlinear integral equations.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Keywords
(α,β)-nonexpansive mapping, fixed point, LP spaces, strictly pseudo-contractive mapping
References
J. Math. Anal. Appl., 467(2), 1168-1173.
Aoyama, K. and Kohsaka, F. (2011). Fixed point theorem for -nonexpansive mappings in Banach spaces. Nonlinear Anal., 74, 4387-4391.
Chidume, C. E. (1987). Iterative approximation of fixed points of Lipschitzian strictly pseudo-contractive mappings. Proc. Amer. Soc, 99(2), 283-288.
Garcia-Falset, J., Llorens-Fuster, E., Suzuki, T. (2011). Fixed point theory for a class of generalized nonexpansive mappings. J. Math. Anal. Appl., 375(1), 185-195.
Suzuki, T. (2008). Fixed point theorems and convergence for some generalized nonexpansive mappings. J. Math. Anal. Appl., 340(2), 1088-1095.
Most read articles by the same author(s)
- Cam Tien Truong, Trung Hieu Nguyen, Convergence of hybrid iteration for equilibrium problems and mappings satisfying condition (ø-Eµ) in uniformly convex and uniformly smooth banach spaces , Dong Thap University Journal of Science: No. 27 (2017): Part B - Natural Sciences
- Trung Hieu Nguyen, Ngoc Cam Huynh, Định lí điểm bất động kép cho ánh xạ co suy rộng trên không gian b -Mêtric thứ tự bộ phận , Dong Thap University Journal of Science: No. 10 (2014): Part B - Natural Sciences
- Pham Cam Tu Cao, Trung Hieu Nguyen, Convergence of a two-step iteration process to common fixed points of two asymptotically g-nonexpansive mappings in Banach spaces with graphs , Dong Thap University Journal of Science: Vol. 9 No. 3 (2020): Natural Sciences Issue (Vietnamese)
- Trung Hieu Nguyen, Về định lí điểm bất động trên không gian S-mêtric thứ tự bộ phận , Dong Thap University Journal of Science: No. 3 (2013): Part B - Natural Sciences
- Diem Ngoc Huynh, Trung Hieu Nguyen, Covergence of hybrid algorithms for α-nonexpansive mappings in Hilbert spaces , Dong Thap University Journal of Science: No. 25 (2017): Part B - Natural Sciences
- Trung Hieu Nguyen, Quoc Ai Ho, Về định lí điểm bất động cho lớp ánh xạ Meir-Keeler -co trên không gian Kiểu b-mêtric , Dong Thap University Journal of Science: No. 9 (2014): Part B - Natural Sciences
- Trung Hieu Nguyen, Hien Huong Hoang, Về định lí điểm bất động chung cho ánh xạ trong không gian kiểu-mêtric , Dong Thap University Journal of Science: No. 8 (2014): Part B - Natural Sciences
- Trung Hieu Nguyen, Thi Vui Nguyen, Về định lí điểm bất động cho lớp ánh xạ C-co yếu trong không gian S-mêtric sắp thứ tự , Dong Thap University Journal of Science: No. 7 (2014): Part B - Natural Sciences
- Kim Ngoan Nguyen, Trung Hieu Nguyen, Convergence of agarwal-type iteration process to common fixed points of two generalized -nonexpansive mappings in uniformly convex Banach spaces , Dong Thap University Journal of Science: No. 37 (2019): Part B - Natural Sciences
- Thi Kieu Ngan Doan, Trung Hieu Nguyen, Some common fixed point theorems for -weak nonlinear contraction in partially ordered metric-type spaces , Dong Thap University Journal of Science: No. 13 (2015): Part B - Natural Sciences