Viscosity Methods of Asymptotically Pseudocontractive and Asymptotically Nonexpansive Mappings for Variational Inequalities

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

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

Iterative Methods for Variational Inequalities, Equilibrium Problems, and Asymptotically Strict Pseudocontractive Mappings

In this paper, we introduce iterative algorithms for finding a common element of the set of fixed points for an asymptotically strict pseudocontractive mappings in the intermediate sense, the set of solutions of the variational inequalities for a family of α-inverse-strongly monotone mappings and the set of solutions of a system of equilibrium problems in a Hilbert space. We establish some weak...

Weak Convergence Theorems for Asymptotically Nonexpansive Mappings and Total Asymptotically Nonexpansive Non-Self Mappings

In this paper, we proposed a new two-step iteration scheme of hybrid mixed type for two asymptotically nonexpansive self mappings and two total asymptotically nonexpansive non-self mappings and establish some weak convergence theorems for mentioned scheme and mappings in the setting of uniformly convex Banach spaces. Our results extend and generalize several results from the current existing li...

Convergence theorems for uniformly quasi- -asymptotically nonexpansive mappings, generalized equilibrium problems, and variational inequalities

In this article, we introduce an iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi-asymptotically nonexpansive mappings, the set of the variational inequality for an a-inverse-strongly monotone operator, and the set of solutions of the generalized equilibrium problems. We obtain a strong convergence theorem for...