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1.
In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a generalized equilibrium problem in a real Hilbert space. Then, strong convergence of the scheme to a common element of the two sets is proved. As an application, problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of an equilibrium problem is solved. Moreover, solution is given to the problem of finding a common element of fixed points set of nonexpansive mappings and the set of solutions of a variational inequality problem.  相似文献   

2.
In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an α ‐inverse strongly monotone mapping in a Hilbert space. We show that the sequence converges strongly to a common element of two sets under some mild conditions on parameters (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

3.
The purpose of this paper is to investigate the problem of finding a common element of the set of solutions of a generalized equilibrium problem (for short, GEP) and the set of fixed points of a nonexpansive mapping in the setting of Hilbert spaces. By using well-known Fan-KKM lemma, we derive the existence and uniqueness of a solution of the auxiliary problem for GEP. On account of this result and Nadler’s theorem, we propose an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of GEP and the set of fixed points of a nonexpansive mapping. Furthermore, it is proven that the sequences generated by this iterative scheme converge strongly to a common element of the set of solutions of GEP and the set of fixed points of a nonexpansive mapping.  相似文献   

4.
In this paper, we introduce an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of a nonexpansive mapping, and the the set of solutions of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets, which is a solution of a certain optimization problem related to a strongly positive bounded linear operator.  相似文献   

5.
The purpose of this paper is to investigate the problem of finding a common element of the set of solutions of a mixed equilibrium problem (MEP) and the set of common fixed points of finitely many nonexpansive mappings in a real Hilbert space. First, by using the well-known KKM technique we derive the existence and uniqueness of solutions of the auxiliary problems for the MEP. Second, by virtue of this result we introduce a hybrid iterative scheme for finding a common element of the set of solutions of MEP and the set of common fixed points of finitely many nonexpansive mappings. Furthermore, we prove that the sequences generated by the hybrid iterative scheme converge strongly to a common element of the set of solutions of MEP and the set of common fixed points of finitely many nonexpansive mappings.  相似文献   

6.
In this paper, an extragradient-type method is introduced for finding a common element in the solution set of generalized equilibrium problems, in the solution set of classical variational inequalities and in the fixed point set of strictly pseudocontractive mappings. It is proved that the iterative sequence generated in the purposed extragradient-type iterative process converges weakly to some common element in real Hilbert spaces.  相似文献   

7.
Numerical Algorithms - The purpose of this paper is to study and analyze two different kinds of extragradient-viscosity-type iterative methods for finding a common element of the set of solutions...  相似文献   

8.
In this paper, we introduce and analyze a new hybrid iterative algorithm for finding a common element of the set of solutions of mixed equilibrium problems and the set of fixed points of an infinite family of nonexpansive mappings. Furthermore, we prove some strong convergence theorems for the hybrid iterative algorithm under some mild conditions. We also discuss some special cases. Results obtained in this paper improve the previously known results in this area.  相似文献   

9.
In this paper, we present an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem and the set of fixed points of an infinite family of nonexpansive mappings and the set of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithm has strong convergence under some mild conditions imposed on algorithm parameters.  相似文献   

10.
In this paper, we introduce an iterative scheme by the hybrid methods for finding a common element of the set of fixed points of nonexpansive mappings, the set of solutions of an equilibrium problem and the set of solutions of a variational inequality problem in a Hilbert space. Then, we prove the strongly convergent theorem by a hybrid extragradient method to the common element of the set of fixed points of nonexpansive mappings, the set of solutions of an equilibrium problem and the set of solutions of a variational inequality problem. Our results extend and improve the results of Bnouhachem et al. [A. Bnouhachem, M. Aslam Noor, Z. Hao, Some new extragradient iterative methods for variational inequalities, Nonlinear Analysis (2008) doi:10.1016/j.na.2008.02.014] and many others.  相似文献   

11.
In this paper, we introduce a new general iterative algorithm for finding a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of solutions of a general variational inequality for two inverse-strongly accretive mappings in Banach space. We obtain some strong convergence theorems by a modified extragradient method under suitable conditions. Our results extend the recent results announced by many others.  相似文献   

12.
In this paper, an iterative sequence for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of two relatively nonexpansive multi-valued mappings is introduced. This iterative scheme can be viewed as a multi-valued version of the corresponding one introduced by Zhang et al. (Comput Math Appl 61, 262–276, 2011) for two relatively nonexpansive multi-valued mappings. Finally, strong convergence of this sequence is studied in Banach spaces.  相似文献   

13.
In this paper,we consider an iterative sequence for generalized equilibrium problems and strictly pseudocontractive mappings.We show that the iterative sequence converges strongly to a common element of the solution set of generalized equilibrium problems and of the fixed point set of strictly pseudocontractive mappings.  相似文献   

14.
In this paper, we introduce two iterative sequences for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of an equilibrium problem in a Banach space. Then we study the strong and weak convergence of the sequences.  相似文献   

15.
In this paper, we introduce an iterative process which converges strongly to a common element of a set of common fixed points of finite family of closed relatively quasi-nonexpansive mappings, the solution set of generalized equilibrium problem and the solution set of the variational inequality problem for an α-inverse strongly monotone mapping in Banach spaces.  相似文献   

16.
The purpose of this paper is to study the strong convergence of a general iterative scheme to find a common element of the set of common fixed points of a finite family of nonexpansive mappings, the set of solutions of variation inequalities for a relaxed cocoercive mapping and the set of solutions of an equilibrium problem. Our results extend recent results announced by many others.  相似文献   

17.
The purpose of this paper is to introduce a general iterative method for finding a common element of the solution set of quasi-variational inclusion problems and of the common fixed point set of an infinite family of nonexpansive mappings in the framework Hilbert spaces. Strong convergence of the sequences generated by the purposed iterative scheme is obtained.  相似文献   

18.
The purpose of this paper is to present an iterative scheme by a hybrid method for finding a common element of the fixed points of ?-asymptotically nonexpansive mapping, the set of solutions of the equilibrium problem and the set of solutions of the variational inequality for an inverse strongly monotone operator in the framework of Banach spaces. We show that the iterative scheme converges strongly to a common element of the above three sets under appropriate conditions.  相似文献   

19.
The purpose of this paper is to introduce an iterative algorithm for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed points for an infinite family of strictly pseudo-contractive mappings and the set of common fixed points for nonexpansive semi-groups in Hilbert space. Under suitable conditions some strong convergence theorem are proved. The results presented in the paper extend and improve some recent results.  相似文献   

20.
In this paper, we introduce a new iterative process for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for an α-inverse-strongly-monotone, by combining an modified extragradient scheme with the viscosity approximation method. We prove a strong convergence theorem for the sequences generated by this new iterative process.   相似文献   

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