Fixed-point iteration processes for non-Lipschitzian mappings of asymptotically quasi-nonexpansive type.
Approximation of fixed points of asymptotically pseudocontractive mappings in Banach spaces.
Fixed points of a certain class of mappings in spaces with uniformly normal structure.
Fixed points of demicontinuous nearly Lipschitzian mappings in Banach spaces
We introduce the classes of nearly contraction mappings and nearly asymptotically nonexpansive mappings. The class of nearly contraction mappings includes the class of contraction mappings, but the class of nearly asymptotically nonexpansive mappings contains the class of asymptotically nonexpansive mappings and is contained in the class of mappings of asymptotically nonexpansive type. We study the existence of fixed points and the structure of fixed point sets of mappings of these classes in Banach...
Dual convergences of iteration processes for nonexpansive mappings in Banach spaces
In this paper we establish a dual weak convergence theorem for the Ishikawa iteration process for nonexpansive mappings in a reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm, and then apply this result to study the problem of the weak convergence of the iteration process.
Firmly pseudo-contractive mappings and fixed points
We give some fixed point theorems for firmly pseudo-contractive mappings defined on nonconvex subsets of a Banach space. We also prove some fixed point results for firmly pseudo-contractive mappings with unbounded nonconvex domain in a reflexive Banach space.
Random fixed points for a certain class of asymptotically regular mappings
Let (Ω, σ) be a measurable space and K a nonempty bounded closed convex separable subset of a p-uniformly convex Banach space E for p > 1. We prove a random fixed point theorem for a class of mappings T:Ω×K ∪ K satisfying the condition: For each x, y ∈ K, ω ∈ Ω and integer n ≥ 1, ⃦Tⁿ(ω,x) - Tⁿ(ω,y) ⃦ ≤ aₙ(ω)· ⃦x - y ⃦ + bₙ(ω) ⃦x -Tⁿ(ω,x) ⃦ + ⃦y - Tⁿ(ω,y) ⃦ + cₙ(ω) ⃦x - Tⁿ(ω,y) ⃦ + ⃦y - Tⁿ(ω,x) ⃦, where aₙ, bₙ, cₙ: Ω → [0, ∞) are functions satisfying certain conditions and Tⁿ(ω,x) is the value...
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