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 homogenization of an obstacle problem
Random Markov Mappings.
Random periodic point and fixed point results for random monotone mappings in ordered Polish spaces.
Random three-step iteration scheme and common random fixed point of three operators.
Random trilinear forms and the Schur multiplication of tensors.
Random variational inequalities in the absence of sample path continuity.
Random walks on free products
Let be the product of finite groups each having order and let be the probability measure which takes the value on each element of . In this paper we shall describe the point spectrum of in and the corresponding eigenspaces. In particular we shall see that the point spectrum occurs only for suitable choices of the numbers . We also compute the continuous spectrum of in in several cases. A family of irreducible representations of , parametrized on the continuous spectrum of ,...
Randomly connected dynamical systems - asymptotic stability
We give sufficient conditions for asymptotic stability of a Markov operator governing the evolution of measures due to the action of randomly chosen dynamical systems. We show that the existence of an invariant measure for the transition operator implies the existence of an invariant measure for the semigroup generated by the system.
Randomly Weighted Series of Contractions in Hilbert Spaces.
Range inclusion results for derivations on noncommutative Banach algebras
Let A be a Banach algebra, and let D : A → A be a (possibly unbounded) derivation. We are interested in two problems concerning the range of D: 1. When does D map into the (Jacobson) radical of A? 2. If [a,Da] = 0 for some a ∈ A, is Da necessarily quasinilpotent? We prove that derivations satisfying certain polynomial identities map into the radical. As an application, we show that if [a,[a,[a,Da]]] lies in the prime radical of A for all a ∈ A, then D maps into the radical. This generalizes a result...
Range of operators and regularity of solutions
Range of the generalized Radon transform associated with partial differential operators.
In this work we consider two partial differential operators, define a generalized Radon transform and its dual associated with these operators and characterize its range.