Abstract:
We consider a hybrid projection algorithm basing on the shrinking projection method for two families of relatively weak quasi-nonexpansive mappings. We establish strong convergence theorems for approximating the common fixed point of the set of the common fixed points of such two families and the set of solutions of the variational inequality for an inverse-strongly monotone operator in the framework of Banach spaces. At the end of the paper, we apply our results to consider the problem of finding a solution of the complementarity problem. Our results improve and extend the corresponding results announced by recent results.

Abstract:
We consider a hybrid projection algorithm basing on the shrinking projection method for two families of relatively weak quasi-nonexpansive mappings. We establish strong convergence theorems for approximating the common fixed point of the set of the common fixed points of such two families and the set of solutions of the variational inequality for an inverse-strongly monotone operator in the framework of Banach spaces. At the end of the paper, we apply our results to consider the problem of finding a solution of the complementarity problem. Our results improve and extend the corresponding results announced by recent results.

Abstract:
The purpose of this paper is to introduce a general iterative method for finding solutions of a general system of variational inclusions with Lipschitzian relaxed cocoercive mappings. Strong convergence theorems are established in strictly convex and 2-uniformly smooth Banach spaces. Moreover, we apply our result to the problem of finding a common fixed point of a countable family of strict pseudo-contraction mappings.

Abstract:
The purpose of this paper is to introduce a general iterative method for finding solutions of a general system of variational inclusions with Lipschitzian relaxed cocoercive mappings. Strong convergence theorems are established in strictly convex and 2-uniformly smooth Banach spaces. Moreover, we apply our result to the problem of finding a common fixed point of a countable family of strict pseudo-contraction mappings.

Abstract:
We introduce an iterative scheme for finding a common element of the set of common fixed points of a family of infinitely nonexpansive mappings, and the set of solutions of the variational inequality for an inverse-strongly monotone mapping in a Hilbert space. Under suitable conditions, some strong convergence theorems for approximating a common element of the above two sets are obtained. As applications, at the end of the paper we utilize our results to study the problem of finding a common element of the set of fixed points of a family of infinitely nonexpansive mappings and the set of fixed points of a finite family of k-strictly pseudocontractive mappings. The results presented in the paper improve some recent results of Qin and Cho (2008).

Abstract:
We introduce an iterative scheme for finding a common element of the set of common fixed points of a family of infinitely nonexpansive mappings, and the set of solutions of the variational inequality for an inverse-strongly monotone mapping in a Hilbert space. Under suitable conditions, some strong convergence theorems for approximating a common element of the above two sets are obtained. As applications, at the end of the paper we utilize our results to study the problem of finding a common element of the set of fixed points of a family of infinitely nonexpansive mappings and the set of fixed points of a finite family of -strictly pseudocontractive mappings. The results presented in the paper improve some recent results of Qin and Cho (2008).

Abstract:
We first prove the existence of a solution of the generalized equilibrium problem (GEP) using the KKM mapping in a Banach space setting. Then, by virtue of this result, we construct a hybrid algorithm for finding a common element in the solution set of a GEP and the fixed point set of countable family of nonexpansive mappings in the frameworks of Banach spaces. By means of a projection technique, we also prove that the sequences generated by the hybrid algorithm converge strongly to a common element in the solution set of GEP and common fixed point set of nonexpansive mappings. AMS Subject Classification: 47H09, 47H10

Abstract:
For a countable family of strictly pseudo-contractions, a strong convergence of viscosity iteration is shown in order to find a common fixed point of in either a p-uniformly convex Banach space which admits a weakly continuous duality mapping or a p-uniformly convex Banach space with uniformly Gateaux differentiable norm. As applications, at the end of the paper we apply our results to the problem of finding a zero of accretive operators. The main result extends various results existing in the current literature.

Abstract:
We introduce a general composite algorithm for finding a common element of the set of solutions of a general equilibrium problem and the common fixed point set of a finite family of asymptotically nonexpansive mappings in the framework of Hilbert spaces. Strong convergence of such iterative scheme is obtained which solving some variational inequalities for a strongly monotone and strictly pseudocontractive mapping. Our results extend the corresponding recent results of Yao and Liou (2010).