Sự hội tụ của thuật toán lai ghép cho ánh xạ α-không giãn trong không gian Hilbert
Nội dung chính của bài viết
Tóm tắt
Trong bài báo này, chúng tôi giới thiệu hai thuật toán lai ghép và thiết lập sự hội tụ của chúng cho ánh xạ α-không giãn trong không gian Hilbert. Các kết quả này là sự mở rộng của các kết quả chính trong [2]. Đồng thời, chúng tôi xây dựng ví dụ minh họa cho kết quả đạt được.
Chi tiết bài viết
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Từ khóa
thuật toán lai ghép, ánh xạ α-không giãn, không gian Hilbert
Tài liệu tham khảo
[1]. K. Aoyama and F. Kohsaka (2011), “Fixed point theorem for α -nonexpansive mappings in Banach spaces”, Nonlinear Anal., (74), p. 4387-4391.
[2]. Q. Dong and Y. Lu (2015), “A new hybrid algorithm for a nonexpansive mapping”, Fixed Point Theory Appl., (2015:37), p. 1-7.
[3]. D. V. Hieu (2016), “An extension of hybrid method without extrapolation step to equilibrium problems”, J. Ind. Manag. Optim., p. 1-16, DOI:10.3934/jimo.2017015.
[4]. D. V. Hieu (2016), “Parallel extragradient-proximal methods for split equilibrium problems”, Math. Model. Anal., (21), p. 478-501.
[5]. D. V. Hieu (2017), “New subgradient extragradient methods for common solutions to equilibrium problems”, Comput. Optim. Appl., p. 1-24, DOI 10.1007/s10589-017-9899-4.
[6]. D. V. Hieu (2017), “Parallel hybrid methods for generalized equilibrium problems and asymptotically strictly pseudocontractive mappings”, J. Appl. Math. Comput., (53), p. 531-554.
[7]. D. V. Hieu, P. K. Anh, and L. D. Muu (2017), “Modified hybrid projection methods for finding common solutions to variational inequality problems”, Comput. Optim. Appl., (66), p. 75-96.
[8]. D. V. Hieu, L. D. Muu, and P. K. Anh (2016), “Parallel hybrid extragradient methods for pseudomonotone equilibrium problems and nonexpansive mappings”, Numer. Algorithms., (73), p. 197-217.
[9]. F. Kohsaka and W. Takahashi (2008), “Existence and approximation of fixed points of firmly nonexpansive-type mappings in Banach spaces”, SIAM J. Optim., (19), p. 824-835.
[10]. D. Kong, L. Liu, and Y. Wu (2015), “Best proximity point theorems for α -nonexpansive mappings in Banach spaces”, Fixed Point Theory Appl., (2015:159), p. 1-10.
[11]. C. Matinez-Yanes and H. K. Xu (2006), “Strong convergence of the CQ method for fixed point processes”, Nonlinear Anal., (64), p. 2400-2411.
[12]. C. Mongkolkeha, Y. J. Cho, and P. Kumam (2014), “Weak convergence theorems of iterative sequences in Hilbert spaces”, J. Nonlinear Convex Anal., 15(6), p. 1303-1317.
[13]. K. Nakajo and W. Takahashi (2003), “Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups”, J. Math. Anal. Appl., (279), p. 372-379.
[14]. S. Reich (1979), “Weak convergence theorems for nonexpansive mappings in Banach spaces”, J. Math. Anal. Appl., (67), p. 274-276.
[15]. W. Takahashi, Y. Takeuchi, and R. Kubota (2008), “Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces”, J. Math. Anal. Appl., (341), p. 276-286.
[16]. W. Takahashi (2010), “Fixed point theorems for new nonlinear mappings in a Hilbert space”, J. Nonlinear Convex Anal., (11), p. 79-88.
[2]. Q. Dong and Y. Lu (2015), “A new hybrid algorithm for a nonexpansive mapping”, Fixed Point Theory Appl., (2015:37), p. 1-7.
[3]. D. V. Hieu (2016), “An extension of hybrid method without extrapolation step to equilibrium problems”, J. Ind. Manag. Optim., p. 1-16, DOI:10.3934/jimo.2017015.
[4]. D. V. Hieu (2016), “Parallel extragradient-proximal methods for split equilibrium problems”, Math. Model. Anal., (21), p. 478-501.
[5]. D. V. Hieu (2017), “New subgradient extragradient methods for common solutions to equilibrium problems”, Comput. Optim. Appl., p. 1-24, DOI 10.1007/s10589-017-9899-4.
[6]. D. V. Hieu (2017), “Parallel hybrid methods for generalized equilibrium problems and asymptotically strictly pseudocontractive mappings”, J. Appl. Math. Comput., (53), p. 531-554.
[7]. D. V. Hieu, P. K. Anh, and L. D. Muu (2017), “Modified hybrid projection methods for finding common solutions to variational inequality problems”, Comput. Optim. Appl., (66), p. 75-96.
[8]. D. V. Hieu, L. D. Muu, and P. K. Anh (2016), “Parallel hybrid extragradient methods for pseudomonotone equilibrium problems and nonexpansive mappings”, Numer. Algorithms., (73), p. 197-217.
[9]. F. Kohsaka and W. Takahashi (2008), “Existence and approximation of fixed points of firmly nonexpansive-type mappings in Banach spaces”, SIAM J. Optim., (19), p. 824-835.
[10]. D. Kong, L. Liu, and Y. Wu (2015), “Best proximity point theorems for α -nonexpansive mappings in Banach spaces”, Fixed Point Theory Appl., (2015:159), p. 1-10.
[11]. C. Matinez-Yanes and H. K. Xu (2006), “Strong convergence of the CQ method for fixed point processes”, Nonlinear Anal., (64), p. 2400-2411.
[12]. C. Mongkolkeha, Y. J. Cho, and P. Kumam (2014), “Weak convergence theorems of iterative sequences in Hilbert spaces”, J. Nonlinear Convex Anal., 15(6), p. 1303-1317.
[13]. K. Nakajo and W. Takahashi (2003), “Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups”, J. Math. Anal. Appl., (279), p. 372-379.
[14]. S. Reich (1979), “Weak convergence theorems for nonexpansive mappings in Banach spaces”, J. Math. Anal. Appl., (67), p. 274-276.
[15]. W. Takahashi, Y. Takeuchi, and R. Kubota (2008), “Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces”, J. Math. Anal. Appl., (341), p. 276-286.
[16]. W. Takahashi (2010), “Fixed point theorems for new nonlinear mappings in a Hilbert space”, J. Nonlinear Convex Anal., (11), p. 79-88.