We first introduce the iterative procedure to approximate a common element of the fixed-point set of two quasinonexpansive mappings and the solution set of the system of mixed equilibrium problem SMEP in a real Hilbert space. Next, we prove the weak convergence for the given iterative scheme under certain assumptions. Finally, we apply our results to approximate a common element of the set of c...

and Applied Analysis 3 It is well known that, in an infinite dimensional Hilbert space, the normal Mann iterative algorithm has only weak convergence, in general, even for nonexpansive mappings. Hybrid projection algorithms are popular tool to prove strong convergence of iterative sequences without compactness assumptions. Recently, hybrid projection algorithms have received rapid developments;...

We construct a new iterative scheme by hybrid methods and prove strong convergence theorem for approximation of a common fixed point of two countable families of closed relatively quasinonexpansive mappings which is also a solution to a system of equilibrium problems in a uniformly smooth and strictly convex real Banach space with Kadec-Klee property using the properties of generalized f -proje...

In this article, we present viscosity approximation methods for finding a common point of the set solutions variational inequality problem and fixed points multi-valued quasinonexpansive mapping in Banach space. We also discuss some examples to illustrate facts study convergence behaviour iterative schemes presented herein, numerically.

*Correspondence: [email protected] 1Department of Information Science, Toho University, Miyama, Funabashi, Chiba 274-8510, Japan Full list of author information is available at the end of the article Abstract In this paper, we deal with the Halpern iterative scheme for a strongly quasinonexpansive mapping in the setting of a complete geodesic space with curvature bounded above by one...

In this paper, we construct a new iterative scheme by hybrid projection method and prove strong convergence theorems for approximation of a common element of set of common fixed points of an infinite family of asymptotically quasi-φ-nonexpansive mappings, set of solutions to a variational inequality problem and set of common solutions to a system of generalized mixed equilibrium problems in a u...

0

generalized resolvent equations; variational inclusions; algorithm; convergence; generalized pseudocontractive mapping

In this work we use the Noor iteration process for total asymptotically nonexpansive mapping to establish the strong and $Delta$-convergence theorems in the framework of CAT(0) spaces. By doing this, some of the results existing in the current literature  generalize, unify and extend.

*Correspondence: [email protected] 2Department of Computer Science and Intelligent Systems, Oita University, Dannoharu, Oita-shi, Oita, 870-1192, Japan Full list of author information is available at the end of the article Abstract We study the viscosity approximation method due to Moudafi for a fixed point problem of quasinonexpansive mappings in a Hilbert space. First, we establish a str...