Control functions and total boundedness in the space .
Some sufficient conditions for controllability of nonlinear systems described by differential equation ẋ = f(t,x(t),u(t)) are given.
We discuss here several types of convergence of conditional expectations for unbounded closed convex random sets of the form where is a decreasing sequence of sub-σ-algebras and is a sequence of closed convex random sets in a separable Banach space.
Existence of fixed points of multivalued mappings that satisfy a certain contractive condition was proved by N. Mizoguchi and W. Takahashi. An alternative proof of this theorem was given by Peter Z. Daffer and H. Kaneko. In the present paper, we give a simple proof of that theorem. Also, we define Mann and Ishikawa iterates for a multivalued map with a fixed point and prove that these iterates converge to a fixed point of under certain conditions. This fixed point may be different from...