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 work with the notion of the measure of nonhyperconvexity introduced by Cianciaruso and De Pascale [6] in order to obtain new fixed-point theorems in hyperconvex metric spaces. This class of metric spaces was introduced by Aronszajn and Panitchpakdi [1] in 1956 to study problems on extension of uniformly continuous mappings. Several and interesting properties of these spaces we...

It is defined a class of generalized nonexpansive mappings, which properly contains those by Suzuki in 2008, and that preserves some its fixed point results.

and Applied Analysis 3 Remark 1.1. If E is a reflexive strictly convex and smooth Banach space, then for x, y ∈ E, φ x, y 0 if and only if x y. It is sufficient to show that if φ x, y 0 then x y. From 1.6 , we have ‖x‖ ‖y‖. This implies 〈x, Jy〉 ‖x‖2 ‖Jy‖2. From the definitions of j, we have Jx Jy, that is, x y, see 8, 9 for more details. Let C be a nonempty closed convex subset of a smooth Bana...

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 ...

Throughout this paper, let H be a real Hilbert space with inner product 〈·,·〉 and norm ‖ · ‖. Let C be a nonempty closed convex subset of H , we denote by PC(·) the metric projection from H onto C. It is known that z = PC(x) is equivalent to 〈z− y,x− z〉 ≥ 0 for every y ∈ C. Recall that T : C → C is nonexpansive if ‖Tx− Ty‖ ≤ ‖x− y‖ for all x, y ∈ C. A point x ∈ C is a fixed point of T provided ...

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 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...