*Correspondence: kohlenbach@mathematik. tu-darmstadt.de Department of Mathematics, Technische Universität Darmstadt, Schlossgartenstrasse 7, Darmstadt, 64289, Germany Abstract We examine convergence results for modified Halpern iterations due to Cuntavepanit and Panyanak (Fixed Point Theory Appl. 2011:869458, 2011). Following Kohlenbach and Leuştean (Adv. Math. 231:2525-2556, 2012), we extract ...

This paper presents a new problem solving approach that is able to generate optimal policy solution for finite-state stochastic sequential decision-making problems with high data efficiency. The proposed algorithm iteratively builds and improves an approximate Markov Decision Process (MDP) model along with cost-to-go value approximates by generating finite length trajectories through the state-...

A mapping T : C → C is said to be nonexpansive if ‖Tx − Ty‖ ≤ ‖x − y‖, for all x, y ∈ C. We denote by Fix T {x ∈ C : Tx x} the set of fixed points of T . In the last ten years, many papers have been written on the approximation of fixed point for nonlinear mappings by using some iterative processes see, e.g., 1–18 . An explicit iterative process was initially introduced, in 1967, by Halpern 3 i...

In this paper, we introduce a class of totally quasi-φ-asymptotically nonexpansive nonself multi-valued mapping to modify the Halpern-Mann-type iteration algorithm for a totally quasi-φ-asymptotically nonexpansive nonself multi-valued mapping, which has the strong convergence under a limit condition only in the framework of Banach spaces. Our results are applied to study the approximation probl...

for each x, y ∈ C. For a mapping T of C into itself, we denote by F(T) the set of fixed points of T . We also denote by N and R+ the set of positive integers and nonnegative real numbers, respectively. Baillon [1] proved the first nonlinear ergodic theorem. Let C be a nonempty bounded convex closed subset of a Hilbert spaceH and let T be a nonexpansive mapping of C into itself. Then, for an arb...

*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...