Weak Convergence of a Projection Algorithm for Variational Inequalities and Relatively Nonexpansive Mappings in a Banach Space
Weak Convergence of a Projection Algorithm for Variational Inequalities and Relatively Nonexpansive Mappings in a Banach Space
摘要
In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space. Then we show that the sequence converges weakly to a common element of two sets.
In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space. Then we show that the sequence converges weakly to a common element of two sets.
参考文献14
-
1LIONS J L, STAMPACCHIA G. Variational inequalities [J]. Comm. Pure Appl. Math., 1967, 20: 493-519.
-
2BROWDER F E, PETRYSHYN W V. Construction of fixed points of nonlinear mappings in Hilbert space [J]. J. Math. Anal. Appl., 1967, 20: 197-228.
-
3IIDUKA H, TAKAHASHI W, TOYODA M. Approximation of solutions of variational inequalities for monotone mappings [J]. Panamer. Math. J., 2004, 14(2): 49-61.
-
4LIU Fengshan, NASHED M Z. Regularization of nonlinear ill-posed variational inequalities and convergence rates [J]. Set-Valued Anal., 1998, 6(4): 313-344.
-
5IIDUKA H, TAKAHASHI W. Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings [J]. Nonlinear Anal., 2005, 61(3): 341-350.
-
6MATSUSHITA S, TAKAHASHI W. A strong convergence theorem for relatively nonexpansive mappings in a Banach space [J]. J. Approx. Theory, 2005, 134(2): 257--266.
-
7IIDUKA H, TAKAHASHI W. Weak convergence of a projection algorithm for variational inequalities in a Banach space [J]. J. Math. Anal. Appl., 2008, 339(1): 668-679.
-
8BALL K, CARLEN E A, LIEB E H. Sharp uniform convexity and smoothness inequalities for trace norms [J]. Invent. Math., 1994, 115(3): 463-482.
-
9TAKAHASHI Y, HASHIMOTO K, KATO M. On sharp uniform convexity, smoothness, and strong type, cotype inequalities [J]. J. Nonlinear Convex Anal., 2002, 3(2): 267-281.
-
10AL'BER Y I, REICH S. An iterative method for solving a class of nonlinear operator equations in Banach spaces [J]. Panamer. Math. J., 1994, 4(2): 39-54.
-
1Kan Xu-zhou,Guo Wei-ping.A Weak Convergence Theorem for A Finite Family of Asymptotically Nonexpansive Mappings[J].Communications in Mathematical Research,2014,30(4):295-300.
-
2WEI Li,SU Yong-fu,ZHOU Hai-yun.New iterative schemes for strongly relatively nonexpansive mappings and maximal monotone operators[J].Applied Mathematics(A Journal of Chinese Universities),2010,25(2):199-208.
-
3秦小龙,Sun Young CHO.CONVERGENCE ANALYSIS OF A MONOTONE PROJECTION ALGORITHM IN REFLEXIVE BANACH SPACES[J].Acta Mathematica Scientia,2017,37(2):488-502.
-
4丁夏畦,罗佩珠.WEAK CONVERGENCE OF SOME SERIES[J].Acta Mathematica Scientia,2000,20(4):433-441. 被引量：1
-
5杨光崇.QUASI-WEAK CONVERGENCE WITH APPLICATIONS IN ORDERED BANACH SPACE[J].Applied Mathematics and Mechanics(English Edition),1999,20(11):1291-1296. 被引量：1
-
6刘英.Strong convergence theorem for relatively nonexpansive mapping and inverse-strongly-monotone mapping in a Banach space[J].Applied Mathematics and Mechanics(English Edition),2009,30(7):925-932.
-
7WEI Li,SU Yong-fu,ZHOU Hai-yun.Iterative convergence theorems for maximal monotone operators and relatively nonexpansive mappings[J].Applied Mathematics(A Journal of Chinese Universities),2008,23(3):319-325. 被引量：5
-
8Luisa Di Piazza(Dept of Math, via Archirafi 3490123 Palermo ITALY).WEAK CONVERGENCE OF HENSTOCK INTEGRABLE SEQUENCES[J].数学研究,1994,27(1):148-153.
-
9Guangjun SHEN Xiuwei YIN Dongjin ZHU.Weak convergence to Rosenblatt sheet[J].Frontiers of Mathematics in China,2015,10(4):985-1004. 被引量：2
-
10丁夏畦,罗佩珠.WEAK CONVERGENCE OF SOME DIRICHLET SERIES[J].Acta Mathematica Scientia,2001,21(4):433-439.
