The class of asymptotically nonexpansive maps was introduced by Goebel and Kirk [18] as a generalization of the class of nonexpansive maps. They proved that if K is a nonempty closed convex bounded subset of a real uniformly convex Banach space and T is an asymptotically nonexpansive self-mapping of K , then T has a fixed point. Alber and Guerre-Delabriere have studied in [3–5] weakly contracti...

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

In this paper, we propose a self-adaptive algorithm for solving the split common null point problem and fixed multivalued Bregman quasi-nonexpansive mappings in Banach spaces. We prove that sequence generated by our iterative scheme converges strongly to solution of above-mentioned problems under some suitable conditions. also apply main result feasibility Finally, numerical examples are given ...

In this paper, a new self-adaptive step size algorithm to approximate the solution of split minimization problem and fixed point nonexpansive mappings was constructed, which combined proximal modified Mann’s iterative method with inertial extrapolation. The strong convergence theorem provided in framework Hilbert spaces then proven under some suitable conditions. Our result improved related res...

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 ...