On Asymptotically Quasi-ϕ-Nonexpansive Mappings in the Intermediate Sense

On Asymptotically Quasi-φ-Nonexpansive Mappings in the Intermediate Sense

and Applied Analysis 3 It is easy to see that a quasi-nonexpansive mapping is an asymptotically quasi-nonexpansive mapping with the sequence {1}. T is said to be asymptotically nonexpansive in the intermediate sense if and only if it is continuous, and the following inequality holds: lim sup n→∞ sup x,y∈C (∥ ∥Tx − Tny∥∥ − ∥∥x − y∥∥) ≤ 0. 2.6 T is said to be asymptotically quasi-nonexpansive in ...

Some results on asymptotically quasi-φ-nonexpansive mappings in the intermediate sense and equilibrium problems

Some results on fixed points of asymptotically strict quasi-φ-pseudocontractions in the intermediate sense

*Correspondence: [email protected] 2College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, 650221, China Full list of author information is available at the end of the article Abstract In this paper, a new nonlinear mapping, asymptotically strict quasi-φ-pseudocontraction in the intermediate sense, is introduced. Projection algorithms are considered for ...

Strong convergence theorems for equilibrium problems and quasi-φ-asymptotically nonexpansive mappings in Banach spaces

In this paper, we introduce two modified Mann-type iterative algorithms for finding a common element of the set of common fixed points of a family of quasi-φ-asymptotically nonexpansive mappings and the set of solutions of an equilibrium problem in Banach spaces. Then we study the strong convergence of the algorithms. Our results improve and extend the corresponding results announced by many ot...

Bounds on Iterations of Asymptotically Quasi-nonexpansive Mappings

This paper establishes explicit quantitative bounds on the computation of approximate fixed points of asymptotically (quasi-) nonexpansive mappings f by means of iterative processes. Here f : C → C is a selfmapping of a convex subset C ⊆ X of a uniformly convex normed space X . We consider general Krasnoselski-Mann iterations with and without error terms. As a consequence of our quantitative an...