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Continuous dependence on parameters for second order discrete BVP’s

Marek Galewski, Szymon Głąb (2012)

Open Mathematics

Using Fan’s Min-Max Theorem we investigate existence of solutions and their dependence on parameters for some second order discrete boundary value problem. The approach is based on variational methods and solutions are obtained as saddle points to the relevant Euler action functional.

Convergence of sequences of iterates of random-valued vector functions

Rafał Kapica (2003)

Colloquium Mathematicae

Given a probability space (Ω,, P) and a closed subset X of a Banach lattice, we consider functions f: X × Ω → X and their iterates f : X × Ω X defined by f¹(x,ω) = f(x,ω₁), f n + 1 ( x , ω ) = f ( f ( x , ω ) , ω n + 1 ) , and obtain theorems on the convergence (a.s. and in L¹) of the sequence (fⁿ(x,·)).

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