A Note on Implicit and Explicit Mann Iterative Processes for Asymptotically -Strongly Pseudocontractive Mappings

A Note on Implicit and Explicit Mann Iterative Processes for Asymptotically Φ-Strongly Pseudocontractive Mappings

On the Convergence of Mann and Ishikawa Iterative Processes for Asymptotically φ-Strongly Pseudocontractive Mappings

and Applied Analysis 3 proving: 1 a fixed point theorem for an asymptotically pseudocontractive mapping that is also uniformly L-Lipschitzian and uniformly asymptotically regular, 2 that the set of fixed points of T is closed and convex, and 3 the strong convergence of a CQ-iterative method. The literature on asymptotical-type mappings is very wide see, 7–15 . In 1967, Browder 16 and Kato 17 , ...

On the Convergence of Iterative Processes for Generalized Strongly Asymptotically ϕ-Pseudocontractive Mappings in Banach Spaces

Throughout this paper, we assume that X is a uniformly convex Banach space and X∗ is the dual space of X. Let J denote the normalized duality mapping form X into 2 ∗ given by J x {f ∈ X∗ : 〈x, f〉 ‖x‖2 ‖f‖2} for all x ∈ X, where 〈·, ·〉 denotes the generalized duality pairing. It is well known that if X is uniformly smooth, then J is single valued and is norm to norm uniformly continuous on any b...

On the Convergence of Implicit Iterative Processes for Asymptotically Pseudocontractive Mappings in the Intermediate Sense

and Applied Analysis 3 T is said to be an asymptotically strict pseudocontraction in the intermediate sense if there exists a sequence {kn} ⊂ 1,∞ with kn → 1 as n → ∞ and a constant κ ∈ 0, 1 such that lim sup n→∞ sup x,y∈C (∥ ∥Tx − Tny∥∥2 − kn ∥ ∥x − y∥∥2 − κ∥∥ I − T x − I − T y∥∥2 ) ≤ 0. 1.9 For such a case, T is also said to be an asymptotically κ-strict pseudocontraction in the intermediate ...

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