Some results on asymptotically quasi-phi-nonexpansive mappings in the intermediate sense and Ky Fan inequalities

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

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 ...

Note on Some Results for Asymptotically Pseudocontractive Mappings and Asymptotically Nonexpansive Mappings

Some Results on Asymptotically Hemi-pseudocontractive Mappings in the Intermediate Sense

In this paper, a mapping which is asymptotically hemi-pseudocontractive in the intermediate sense is introduced. Hybrid projection methods are considered for the class of mappings. Strong convergence theorems for common fixed points are established in the framework of Hilbert spaces.

Asymptotically Pseudocontractive and Asymptotically Nonexpansive Mappings for Variational Inequalities

and Applied Analysis 3 limn→∞tn 1, ∑∞ n 1 tn 1 − tn ∞, and limn→∞ kn − 1 / kn − tn 0, where ξn min{ 1 − α kn/ kn − α , 1/kn}. For an arbitrary z0 ∈ K let the sequence {zn} be iteratively defined by zn 1 ( 1 − tn kn ) f zn tn kn Tzn, n ∈ N. 1.7 Then i for each integer n ≥ 0, there is a unique xn ∈ K such that xn ( 1 − tn kn ) f xn tn kn Txn; 1.8