In this work, we consider a general algorithm for a countable family of nonexpansive mappings in Banach spaces. We proved that the proposed algorithm converges strongly to a common fixed point of a countable family of nonexpansive mappings which solves uniquely the corresponding variational inequality. It is worth pointing out that our proofs contain some new techniques. Our results improve and...

In this paper, we present some common fixed point theorems for two generalized nonexpansive multivalued mappings in CAT(0) spaces as well as in UCED Banach spaces. Moreover, we prove the existence of fixed points for generalized nonexpansive multivalued mappings in complete geodesic metric spaces with convex metric for which the asymptotic center of a bounded sequence in a bounded closed convex...

In this paper, we consider some iteration processes for one-parameter continuous semigroups of nonexpansive mappings in a nonempty compact convex subset C of a complete CAT(0) space X and prove that the proposed sequence converges to a common fixed point for these semigroups of nonexpansive mappings. Note that our results generalize Cho et al. result (Nonlinear Anal. 74:6050-6059, 2011) and rel...

Recently, the author, together with L. Leustean and A. Nicolae, introduced notion of jointly firmly nonexpansive families mappings in order to investigate an abstract manner convergen...

In this article, we deal with iterative methods for approximation of fixed points and their applications. We first discuss fixed point theorems for a nonexpansive mapping or a family of nonexpansive mappings. In particular, we state a fixed point theorem which answered affirmatively a problem posed during the Conference on Fixed Point Theory and Applications held at CIRM, Marseille-Luminy, 1989...

In this paper, several $Delta$ and strong convergence theorems are established for the Ishikawa iterations for nonexpansive mappings in the framework of CAT(0) spaces. Our results extend and improve the corresponding results

where / is a mapping of X into its adjoint space X* such that for all u in X, (J(u)} ^)=|M| 2 d ||/(^)|| HMI* In some recent papers ([7], [8], [9]), we have presented an existence theory for solutions of nonlinear functional equations in uniformly convex Banach spaces X involving nonexpansive and accretive mappings. These results were obtained by interweaving the fixed point theory of nonexpans...

In this paper we introduce a hybrid relaxed-extragradient method for finding a common element of the set of common fixed points of N nonexpansive mappings and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping. The hybrid relaxed-extragradient method is based on two well-known methods: hybrid and extragradient. We derive a strong convergence ...

Smooth convex optimization problems are solved over fixed point sets of quasi-nonexpansive mappings by using a distributed optimization technique. This is done for a networked system with an operator, who manages the system, and a finite number of users, by solving the problem of minimizing the sum of the operator’s and users’ differentiable, convex objective functions over the intersection of ...

The influence of fixed point theorems for contractive and nonexpansive mappings see 1, 2 on fixed point theory is so huge that there are many results dealing with fixed points of mappings satisfying various types of contractive and nonexpansive conditions. On the other hand, it is also huge that well-known Brouwer’s and Schauder’s fixed point theorems for set-contractive mappings exert an influ...