We consider a concave iteration semigroup of linear continuous set-valued functions defined on a closed convex cone in a separable Banach space. We prove that such an iteration semigroup has a selection which is also an iteration semigroup of linear continuous functions. Moreover it is majorized by an "exponential" family of linear continuous set-valued functions.
For a stochastic process with state space some Polish space, this paper gives sufficient conditions on the initial and conditional distributions for the joint law to satisfy Gaussian concentration inequalities and transportation inequalities. In the case of the Euclidean space , there are sufficient conditions for the joint law to satisfy a logarithmic Sobolev inequality. In several cases, the constants obtained are of optimal order of growth with respect to the number of random variables, or are...
In this note we study questions of redundancy concerning the functional equation f(h(x)+k(x)) = f(h(x))+f(k(x)), where h and k are given functions and f is the unknown function.
Using the fixed point theorems of Banach and Schauder we discuss the existence, uniqueness and stability of continuous solutions of a polynomial-like iterative equation with variable coefficients.