Determining xed points of nonexpansive mappings is a frequent problem in mathematics and physical sciences. An algorithm for nding common xed points of nonexpansive mappings in Hilbert space, essentially due to Halpern, is analyzed. The main theorem extends Wittmann's recent work and partially generalizes a result by Lions. Algorithms of this kind have been applied to the convex feasibility pro...

In this paper, based on a generalized projection, we introduce a new modified Halpern-type iteration algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of a common fixed point of an infinitely countable family of relatively quasi-nonexpansive mappings in the framework of Banach spaces. We establish the strong convergence theorem and obtain some ...

* Correspondence: [email protected] Department of Mathematics, Faculty of Science, Imam Khomeini International University, P.O. Box 34149-16818, Qazvin, Iran Full list of author information is available at the end of the article Abstract In this paper, an iterative sequence for relatively nonexpansive multi-valued mappings by using the notion of generalized projection is introduced, and th...

The propose of this paper is to present a modified block iterative algorithm for finding a common element between the set of solutions of the fixed points of two countable families of asymptotically relatively nonexpansive mappings and the set of solution of the system of generalized mixed equilibrium problems in a uniformly smooth and uniformly convex Banach space. Our results extend many know...

* Correspondence: smkang@gnu. ac.kr Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Korea Full list of author information is available at the end of the article Abstract In this paper, an implicit iterative algorithm with errors is considered for two families of generalized asymptotically nonexpansive mappings. Strong and weak convergence theorems of common fi...

In this paper, we are concerned with the study of a multi-step iterative scheme with errors insolving a finite family of asymptotically quasinonexpansive self-mappings. We approximate the common fixed points of a finite family of asymptotically quasi-nonexpansive self-mappings by convergence of the scheme in a uniformly convex Banach space. Our results extend and improve some recent results, Q....

We prove a strong convergence result for a sequence generated by Halpern's type iteration for approximating a common fixed point of a countable family of quasi-Lipschitzian mappings in a real Hilbert space. Consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

We introduce the new generalized mixed equilibrium problem with respect to relaxed semimonotone mappings. Using the KKM technique, we obtain the existence of solutions for the generalizedmixed equilibriumproblem in Banach spaces. Furthermore, we also introduce a hybrid projection algorithm for finding a common element in the solution set of a generalized mixed equilibrium problem and the fixed ...

The theory of modular spaces was initiated by Nakano 1 in 1950 in connection with the theory of order spaces and redefined and generalized by Musielak and Orlicz 2 in 1959. These spaces were developed following the successful theory of Orlicz spaces, which replaces the particular, integral form of the nonlinear functional, which controls the growth of members of the space, by an abstractly give...