Strong convergence theorems for countable families of multivalued nonexpansive mappings and systems of equilibrium and variational inequality problems

被引:0
作者
Shehu Y. [1 ]
机构
[1] Department of Mathematics, University of Nigeria, Nsukka
关键词
Equilibrium problem; Hilbert spaces; Multi valued nonexpansive mapping; Strong convergence; Variational inequality;
D O I
10.1007/s11565-012-0156-6
中图分类号
学科分类号
摘要
In this paper, we introduce a new iterative scheme by hybrid methods and prove strong convergence of the scheme for approximation of a common fixed point of two countably infinite families of multi valued nonexpansive mappings which is also a solution to system equilibrium problems and system of variational inequality problems in a real Hilbert space. Our results extend important recent results. © 2012 Università degli Studi di Ferrara.
引用
收藏
页码:371 / 387
页数:16
相关论文
共 30 条
[1]  
Blum E., Oettli W., From optimization and variational inequalities to equilibrium problems, Math. Stud., 63, pp. 123-145, (1994)
[2]  
Browder F.E., Petryshyn W.V., Construction of fixed points of nonlinear mappings in Hilbert spaces, J. Math. Anal. Appl., 20, pp. 197-228, (1967)
[3]  
Bruck R.E., On weak convergence of an ergodic iteration for the solution of variational inequalities for monotone operators in Hilbert space, J. Math. Anal. Appl., 61, pp. 159-164, (1977)
[4]  
Ceng L.C., Khan A.R., Ansari Q.H., Yao J.C., Viscosity approximation methods for strongly positive and monotone operators, Fixed Point Theory., 10, 1, pp. 35-71, (2009)
[5]  
Cholamjiak W., Suantai S., A hybrid method for a countable family of multivalued maps, equilibrium problems and variational inequality problems, Discrete Dyn. Nat. Soc., 2010, (2010)
[6]  
Combettes P.L., Hirstoaga S.A., Equilibrium programming in Hilbert spaces, J. Nonlinear Convex Anal., 6, pp. 117-136, (2005)
[7]  
Genel A., Linderstrauss J., An example concerning fixed points, Israel. J. Math., 22, pp. 81-86, (1975)
[8]  
Iiduka H., Takahashi W., Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings, Nonlinear Anal., 61, pp. 341-350, (2005)
[9]  
Kumam P., A new hybrid iterative method for solution of equilibrium problems and fixed point problems for an inverse strongly monotone operator and a nonexpansive mapping, J. Appl. Math. Comput., 29, pp. 263-280, (2009)
[10]  
Kumam P., Katchang P., A viscosity of extragradient approximation method for finding equilibrium problems, variational inequalities and fixed point problems for nonexpansive mappings, Nonlinear Anal. Hybrid Syst., 3, pp. 475-486, (2009)