Convergence Theorem of Hybrid Iterative Algorithm for Equilibrium Problems and Fixed Point Problems of Finite Families of Uniformly Asymptotically Nonexpansive Semigroups

作者: Hongbo Liu , Yi Li

DOI: 10.4236/APM.2014.46033

关键词:

摘要: Throughout this paper, we introduce a new hybrid iterative algorithm for finding common element of the set common fixed points finite family uniformly asymptotically nonexpansive semigroups and solutions an equilibrium problem in framework Hilbert spaces. We then prove strong convergence theorem with respect to proposed algorithm. Our results this paper extend improve some recent known results.

参考文章(20)
W Oettli, E. Blum, From optimization and variational inequalities to equilibrium problems Math. Student. ,vol. 63, pp. 123- 145 ,(1994)
Tomonari Suzuki, On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces Proceedings of the American Mathematical Society. ,vol. 131, pp. 2133- 2136 ,(2002) , 10.1090/S0002-9939-02-06844-2
Huimin He, Rudong Chen, Strong Convergence Theorems of the CQ Method for Nonexpansive Semigroups Fixed Point Theory and Applications. ,vol. 2007, pp. 059735- ,(2007) , 10.1155/2007/59735
Ştefan Măruşter, Cristina Popirlan, None, On the Mann-type iteration and the convex feasibility problem Journal of Computational and Applied Mathematics. ,vol. 212, pp. 390- 396 ,(2008) , 10.1016/J.CAM.2006.12.012
Kazuhide Nakajo, Wataru Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups Journal of Mathematical Analysis and Applications. ,vol. 279, pp. 372- 379 ,(2003) , 10.1016/S0022-247X(02)00458-4
Dan Butnariu, Yair Censor, Pini Gurfil, Ethan Hadar, On The Behavior of Subgradient Projections Methods for Convex Feasibility Problems in Euclidean Spaces Siam Journal on Optimization. ,vol. 19, pp. 786- 807 ,(2008) , 10.1137/070689127
Elaine T. Hale Wotao Yin and Yin Zhang, FIXED-POINT CONTINUATION APPLIED TO COMPRESSED SENSING: IMPLEMENTATION AND NUMERICAL EXPERIMENTS * Journal of Computational Mathematics. ,(2010) , 10.4208/JCM.2009.10-M1007
Wataru Takahashi, Yukio Takeuchi, Rieko Kubota, Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces Journal of Mathematical Analysis and Applications. ,vol. 341, pp. 276- 286 ,(2008) , 10.1016/J.JMAA.2007.09.062
Heinz H. Bauschke, Jonathan M. Borwein, On Projection Algorithms for Solving Convex Feasibility Problems SIAM Review. ,vol. 38, pp. 367- 426 ,(1996) , 10.1137/S0036144593251710