Let C be a closed convex subset of a Banach space E. A mapping T on C is called a nonexpansive mapping if ‖Tx−Ty‖ ≤ ‖x− y‖ for all x, y ∈ C. We denote by F(T) the set of fixed points of T . Kirk [17] proved that F(T) is nonempty in the case that C is weakly compact and has normal structure. See also [2, 3, 5, 6, 11] and others. Convergence theorems to fixed points are also proved by many author...

In this paper, we suggest and analyze both explicit and implicit iterative schemes for two strongly positive operators and a nonexpansive mapping S on a Hilbert space. We also study explicit and implicit versions of iterative schemes for an inverse-strongly monotone mapping T and S by an extragradient-like approximation method. The viscosity approximation methods are employed to establish stron...

We introduce a concept of weak Bregman relatively nonexpansive mapping which is distinct from Bregman relatively nonexpansive mapping. By using projection techniques, we construct several modification of Mann type iterative algorithms with errors and Halpern-type iterative algorithms with errors to find fixed points of weak Bregman relatively nonexpansive mappings and Bregman relatively nonexpa...

and Applied Analysis 3 Remark 1.2. i Since 0 αn βn 1, n 1 and ∑∞ n 1 αnβn ∞, the iterative sequence 1.6 could not be reduced to a Mann iterative sequence 1.4 . Therefore, the iterative sequence 1.6 has some particular cases. ii The iterative sequence 1.6 is usually called the Ishikawa iterative sequence. iii Chidume andMutangadura 17 gave an example to show that the Mann iterative sequence fail...

We look for geometric structures which underlie both the 'classical' geometric and more modern 'order theoretic' conditions for a Banach space (dual space) to have the weak (weak*) fixed point property; that is, for every nonexpansive self-mapping of a nonempty weak (weak*) compact convex subset to have a fixed point.

In this paper, we study the Picard-Mann hybrid iteration process to approximate fixed points of Suzuki's generalized nonexpansive mappings. We establish some weak and strong convergence theorems for such mappings in uniformly convex Banach space.

* Correspondence: [email protected]. edu.tw Department of Mathematics, National Changhua University of Education, Changhua, 50058, Taiwan Full list of author information is available at the end of the article Abstract In this paper, we introduce generalized hybrid mapping on CAT(0) spaces. The class of generalized hybrid mappings contains the class of nonexpansive mappings, nonspreading mappings,...

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...

Let P be a cone in a Hilbert space H, A : P → 2 be an accretive mapping (equivalently, −A be a dissipative mapping) and T : P → P be a nonexpansive mapping. In this paper, some fixed point theorems for mappings of the type −A+T are established. As an application, we utilize the results presented in this paper to study the existence problem of solutions for some kind of nonlinear integral equati...