A viscosity method for solving convex feasibility problems
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Authors
Yunpeng Zhang
- College of Electric Power, North China University of Water Resources and Electric Power, Zhengzhou, 450011, China.
Yanling Li
- School of Mathematics and Information Sciences, North China University of Water Resources and Electric Power University, Zhengzhou 450011, China.
Abstract
In this paper, generalized equilibrium problems and strict pseudocontractions are investigated based on a
viscosity algorithm. Strong convergence theorems are established in the framework of real Hilbert spaces.
Share and Cite
ISRP Style
Yunpeng Zhang, Yanling Li, A viscosity method for solving convex feasibility problems, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 2, 641--651
AMA Style
Zhang Yunpeng, Li Yanling, A viscosity method for solving convex feasibility problems. J. Nonlinear Sci. Appl. (2016); 9(2):641--651
Chicago/Turabian Style
Zhang, Yunpeng, Li, Yanling. "A viscosity method for solving convex feasibility problems." Journal of Nonlinear Sciences and Applications, 9, no. 2 (2016): 641--651
Keywords
- Equilibrium problem
- variational inequality
- nonexpansive mapping
- fixed point
- viscosity algorithm.
MSC
References
-
[1]
B. A. Bin Dehaish, A. Latif, H. Bakodah, X. Qin , A regularization projection algorithm for various problems with nonlinear mappings in Hilbert spaces, J. Inequal. Appl., 2015 (2015), 14 pages.
-
[2]
B. A. Bin Dehaish, X. Qin, A. Latif, H. Bakodah , Weak and strong convergence of algorithms for the sum of two accretive operators with applications, J. Nonlinear Convex Anal., 16 (2015), 1321-1336.
-
[3]
E. Blum, W. Oettli , From optimization and variational inequalities to equilibrium problems, Math. Student, 63 (1994), 123-145.
-
[4]
F. E. Browder, W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl., 20 (1967), 197-228.
-
[5]
S. S. Chang , Viscosity approximation methods for a finite family of nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., 323 (2006), 1402-1416.
-
[6]
S. S. Chang, H. W. J. Lee, C. K. Chan, Strong convergence theorems by viscosity approximation methods for accretive mappings and nonexpansive mappings, J. Appl. Math. Informatics, 27 (2009), 59-68.
-
[7]
S. Y. Cho, S. M. Kang, Approximation of fixed points of pseudocontraction semigroups based on a viscosity iterative process, Appl. Math. Lett., 24 (2011), 224-228.
-
[8]
S. Y. Cho, X. Qin, On the strong convergence of an iterative process for asymptotically strict pseudocontractions and equilibrium problems , Appl. Math. Comput., 235 (2014), 430-438.
-
[9]
S. Y. Cho, X. Qin, S. M. Kang , Iterative processes for common fixed points of two different families of mappings with applications, J. Global Optim., 57 (2013), 1429-1446.
-
[10]
S. Y. Cho, X. Qin, L. Wang, Strong convergence of a splitting algorithm for treating monotone operators, Fixed Point Theory Appl., 2014 (2014), 15 pages.
-
[11]
H. O. Fattorini, Infinite-dimensional optimization and control theory, Cambridge University Press, Cambridge (1999)
-
[12]
R. H. He, Coincidence theorem and existence theorems of solutions for a system of Ky Fan type minimax inequalities in FC-spaces, Adv. Fixed Point Theory, 2 (2012), 47-57.
-
[13]
Z. He, C. Chen, F. Gu, Viscosity approximation method for nonexpansive nonself-mapping and variational inequality, J. Nonlinear Sci. Appl., 1 (2008), 169-178.
-
[14]
J. S. Jung, Viscosity approximation methods for a family of finite nonexpansive mappings in Banach spaces, Nonlinear Anal., 64 (2006), 2536-2552.
-
[15]
J. K. Kim, S. Y. Cho, X. Qin, Some results on generalized equilibrium problems involving strictly pseudocontractive mappings, Acta Math. Sci. Ser. B, Engl. Ed., 31 (2011), 2041-2057.
-
[16]
L. S. Liu , Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl., 194 (1995), 114-125.
-
[17]
S. Lv, Strong convergence of a general iterative algorithm in Hilbert spaces, J. Inequal. Appl., 2013 (2013), 18 pages.
-
[18]
A. Moudafi, Viscosity approximation methods for fixed-points problems, J. Math. Anal. Appl., 241 (2000), 46-55.
-
[19]
L. P. Pang, J. Shen, An approximate bundle method for solving variational inequalities, Commun. Optim. Theory, 1 (2012), 1-18.
-
[20]
X. Qin, S. Y. Cho, L. Wang, Convergence of splitting algorithms for the sum of two accretive operators with applications, Fixed Point Theory Appl., 2014 (2014), 12 pages.
-
[21]
X. Qin, S. Y. Cho, L. Wang, A regularization method for treating zero points of the sum of two monotone operators, Fixed Point Theory Appl., 2014 (2014), 10 pages
-
[22]
X. Qin, M. Shang, Y. Su , Strong convergence of a general iterative algorithm for equilibrium problems and variational inequality problems, Math. Comput. Modelling, 48 (2008), 1033-1046.
-
[23]
X. Qin, Y. Su, L. Wang, Iterative algorithms with errors for zero points of m-accretive operators, Fixed Point Theory Appl., 2013 (2013), 17 pages.
-
[24]
Y. Qing, S. Lv, Strong convergence of a parallel iterative algorithm in a reflexive Banach space, Fixed Point Theory Appl., 2014 (2014), 9 pages.
-
[25]
T. Suzuki , Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semi-groups without Bochner integrals, J. Math. Anal. Appl., 305 (2005), 227-239.
-
[26]
S. Takahashi, W. Takahashi , Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl., 331 (2007), 506-515.
-
[27]
Y. Yao, M. A. Noor , On viscosity iterative methods for variational inequalities, J. Math. Anal. Appl., 325 (2007), 776-787.
-
[28]
J. Ye, J. Huang, An iterative method for mixed equilibrium problems, fixed point problems of strictly pseudo-contractive mappings and nonexpansive semi-group, Nonlinear Funct. Anal. Appl., 18 (2013), 307-325.
-
[29]
M. Zhang, Strong convergence of a viscosity iterative algorithm in Hilbert spaces, J. Nonlinear Funct. Anal., 2014 (2014), 16 pages.
-
[30]
L. Zhang, H. Tong, An iterative method for nonexpansive semigroups, variational inclusions and generalized equilibrium problems, Adv. Fixed Point Theory, 4 (2014), 325-343.
-
[31]
J. Zhao , Strong convergence theorems for equilibrium problems, fixed point problems of asymptotically nonexpansive mappings and a general system of variational inequalities, Nonlinear Funct. Anal. Appl., 16 (2011), 447-464.