This paper introduces a composite iteration scheme for approximating a fixed point of nonexpansive mappings in the framework of uniformly smooth Banach spaces and the reflexive Banach spaces which have a weakly contin...This paper introduces a composite iteration scheme for approximating a fixed point of nonexpansive mappings in the framework of uniformly smooth Banach spaces and the reflexive Banach spaces which have a weakly continuous duality map, respectively, we establish the strong convergence of the composite iteration scheme. The results improve and extend those of Kim, Xu, Wittmann and some others.展开更多
The purpose of this paper is to present a general iterative scheme as below：{F（un,y）＋1/rn（y-un,un-xn）≥0,y∈C,xn＋1=（I-αnA）Sun＋αnγf（xn）and to prove that, if {an} and {rn} satisfy appropriate conditions, ...The purpose of this paper is to present a general iterative scheme as below：{F（un,y）＋1/rn（y-un,un-xn）≥0,y∈C,xn＋1=（I-αnA）Sun＋αnγf（xn）and to prove that, if {an} and {rn} satisfy appropriate conditions, then iteration sequences {xn} and {un} converge strongly to a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping and the set of solution of a variational inequality, too. Furthermore, by using the above result, we can also obtain an iterative algorithm for solution of an optimization problem min h（x）, where h（x） is a convex and lower semicontinuous functional defined on a closed convex subset C of a Hilbert space H. The results presented in this paper extend, generalize and improve the results of Combettes and Hirstoaga, Wittmann, S.Takahashi, Giuseppe Marino, Hong-Kun Xu, and some others.展开更多
基金The project is supported by National Natural Science Foundation of China under Grant No. 60574005.
文摘This paper introduces a composite iteration scheme for approximating a fixed point of nonexpansive mappings in the framework of uniformly smooth Banach spaces and the reflexive Banach spaces which have a weakly continuous duality map, respectively, we establish the strong convergence of the composite iteration scheme. The results improve and extend those of Kim, Xu, Wittmann and some others.
基金supported by the National Natural Science Foundation of China under Grant No. 10771050.
文摘The purpose of this paper is to present a general iterative scheme as below：{F（un,y）＋1/rn（y-un,un-xn）≥0,y∈C,xn＋1=（I-αnA）Sun＋αnγf（xn）and to prove that, if {an} and {rn} satisfy appropriate conditions, then iteration sequences {xn} and {un} converge strongly to a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping and the set of solution of a variational inequality, too. Furthermore, by using the above result, we can also obtain an iterative algorithm for solution of an optimization problem min h（x）, where h（x） is a convex and lower semicontinuous functional defined on a closed convex subset C of a Hilbert space H. The results presented in this paper extend, generalize and improve the results of Combettes and Hirstoaga, Wittmann, S.Takahashi, Giuseppe Marino, Hong-Kun Xu, and some others.
