The purpose of this paper is to investigate nonemptyness of the solution set for generalized mixed quasi-equilibrium problems and investigate the asymptotic behavior of an iterative algorithm for finding common solution of generalized mixed equilibrium problems and fixed point problems of asymptotically nonexpansive mappings under mild conditions of iteration parameters. Our results improve and...

We introduce viscosity approximations by using the shrinking projection method established by Takahashi, Takeuchi, and Kubota, for finding a common element of the set of solutions of the generalized equilibrium problem and the set of fixed points of a quasi-nonexpansive mapping. Furthermore, we also consider the viscosity shrinking projection method for finding a common element of the set of so...

The purpose of this paper is to establish some strong convergence theorems of three-step iteration process with errors for approximating common fixed points for a finite family of asymptotically quasi-nonexpansive mappings in the intermediate sense in the setting of convex metric spaces. The results obtained in this paper generalize, improve and unify some main results of [1]-[7], [9]-[11], [13...

In this paper, we prove the strong convergence of an implicit iterative scheme with errors to a common fixed point for a finite family of generalized asymptotically quasi-nonexpansive mappings in convex metric spaces. Our results refine and generalize several recent and comparable results in uniformly convex Banach spaces. With the help of an example we compare implicit iteration used in our re...

We introduce an iterative scheme for finding a common element of the set of solutions of generalizedmixed equilibrium problems and the set of fixed points for countable families of total quasi-φasymptotically nonexpansive mappings in Banach spaces. We prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm in an uniformly smooth and strictly co...

for all x, y ∈ C and each n ≥ 1. The class of asymptotically nonexpansive mappings was introduced by Goebel and Kirk [1] as an important generalization of nonexpansive mappings. It was proved in [1] that if C is a nonempty bounded closed convex subset of a real uniformly convex Banach space and T is an asymptotically nonexpansive self mapping on C, then F (T ) is nonempty closed convex subset o...

An iterative algorithm is introduced to solve the split common fixed point problems for asymptotically quasi-nonexpansive mappings in Hilbert spaces. The strong and weak convergence of the presented algorithm to some split common fixed point are obtained. The results presented in this paper improve and extend some recent results of Moudafi [Nonlinear Anal. 74 (2011), 4083-4087], Xu [Inverse Pro...

The purpose of this paper is to study sufficient and necessary conditions for finite-step iterative sequences withmean errors for a finite family of asymptotically quasi-nonexpansive and type mappings in Banach spaces to converge to a common fixed point. The results presented in this paper improve and extend the recent ones announced by GhostDebnath, Liu, Xu and Noor, Chang, Shahzad et al., Sha...

The purpose of this paper is to propose a modified hybrid projection algorithm and prove a strong convergence theorem for a family of quasi-φ-nonexpansive mappings. The strong convergence theorem is proven in the more general reflexive, strictly convex, and smooth Banach spaces with the property K . The results of this paper improve and extend the results of S. Matsushita and W. Takahashi 2005 ...