We prove Browder’s type strong convergence theorems for infinite families of nonexpansive mappings. One of our main results is the following: let C be a bounded closed convex subset of a uniformly smooth Banach space E. Let {Tn : n ∈ N} be an infinite family of commuting nonexpansive mappings on C. Let {αn} and {tn} be sequences in (0,1/2) satisfying limn tn = limn αn/t n = 0 for ∈ N. Fix u ∈ C...

* Correspondence: changss@yahoo. cn; [email protected] Department of Mathematics, Yibin university, Yibin, Sichuan 644007, China Department of Mathematics, College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China Full list of author information is available at the end of the article Abstract The purpose of this article is to introduc...

The purpose of this paper is, by using a new hybrid method, to prove a strong convergence theorem for finding a common element of the set of solutions for a generalized mixed equilibrium problem, the set of solutions for a variational inequality problem, and the set of common fixed points for a pair of quasi-φ-asymptotically nonexpansive mappings. Under suitable conditions some strong convergen...

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...

In this paper our aim is to introduce a new class of procedure, the Uniformly Asymptotically Regular-class of procedures (UAR-precedures), showing some examples of procedures as for finite family of mappings, as for infinite family of mappings. Then by a UAR-procedure we prove the convergence of an implicit iterative method and of an explicit iterative method to the unique solution of a variati...

In this paper, we introduce a modified three-step iterative 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 modified three-step iterative scheme. The results improve and extend recent ones given by...

The purpose of this paper is first to introduce the concept of total quasi-φ-asymptotically nonexpansive mapping which contains many kinds of mappings as its special cases and then to use a hybrid algorithm to introduce a new iterative scheme for finding a common element of the set of solutions for a system of generalized mixed equilibrium problems and the set of common fixed points for a count...

In this paper, we analyze a three-step iterative scheme for three strongly pseudocontractive mappings in a uniformly smooth Banach space. Our results can be viewed as an extension of three-step and two-step iterative schemes of Glowinski and Le Tallec [3], Noor [1215] and Ishikawa [7], Liu [10] and Xu [20]. 2000 Mathematics Subject Classification: Primary 47H10, 47H17: Secondary 54H25

Two iterative schemes for finding a common element of the set of zero points of maximal monotone operators and the set of fixed points of nonexpansive mappings in the sense of Lyapunov functional in a real uniformly smooth and uniformly convex Banach space are obtained. Two strong convergence theorems are obtained which extend some previous work. Moreover, the applications of the iterative sche...

In this paper we show the weak convergence and stability of the proximal point method when applied to the constrained convex optimization problem in uniformly convex and uniformly smooth Banach spaces. In addition, we establish a nonasymptotic estimate of convergence rate of the sequence of functional values for the unconstrained case. This estimate depends on a geometric characteristic of the ...