Random fixed point theorems for nonexpansive and contractive-type random operators on Banach spaces.
Random Fixed Point Theorems For Ultimately Compact Operators.
Random fixed point theorems on product spaces.
Random fixed point theory in spaces with two metrics.
Random fixed points and approximations in random convex metric spaces.
Random fixed points and random differential inclusions.
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...
Random fixed points for *-nonexpansive random operators.
Random fixed points of increasing compact random maps
Let be a measurable space, be an ordered separable Banach space and let be a nonempty order interval in . It is shown that if is an increasing compact random map such that and for each then possesses a minimal random fixed point and a maximal random fixed point .
Random fixed points of multivalued inward random operators.
Random fixed points of multivalued maps in Fréchet spaces
In this paper we prove a general random fixed point theorem for multivalued maps in Frechet spaces. We apply our main result to obtain some common random fixed point theorems. Our main result unifies and extends the work due to Benavides, Acedo and Xu [4], Itoh [8], Lin [12], Liu [13], Tan and Yuan [20], Xu [23], etc.
Random fixed points of non-self maps and random approximations.
Random fixed points of weakly inward operators in conical shells.
Random three-step iteration scheme and common random fixed point of three operators.
Ray's theorem for firmly nonexpansive-like mappings and equilibrium problems in Banach spaces.
Reflexive Banach space and fixed point theorems.
Reflexivity and approximate fixed points
A Banach space X is reflexive if and only if every bounded sequence xₙ in X contains a norm attaining subsequence. This means that it contains a subsequence for which is attained at some f in the dual unit sphere . A Banach space X is not reflexive if and only if it contains a normalized sequence xₙ with the property that for every , there exists such that . Combining this with a result of Shafrir, we conclude that every infinite-dimensional Banach space contains an unbounded closed convex...
Régularisation pour les problèmes à opérateurs monotones et la méthode de Galerkin
Regularization and error estimates for nonhomogeneous backward heat problems.
Regularization and new error estimates for a modified Helmholtz equation.