Selections of multifunctions of two variables

Increasing Selections from Increasing Multifunctions

We study when the existence of an increasing selection can be derived from the monotonicity of a multifunction w.r.t. an extension of the basic order from points to subsets. The most interesting results emerge when the target is a lattice and monotonicity is interpreted in one of the ways suggested by A.F. Veinott, Jr. An increasing selection exists if (1) the multifunction is weakly ascending ...

Representations of Affine Multifunctions by Affine Selections

The paper deals with affine selections of affine (both convex and concave) multifunctions acting between finite-dimensional real normed spaces. It is proved that each affine multifunction with compact values possesses an exhaustive family of affine selections and, consequently, can be represented by its affine selections. Moreover, a convex multifunction with compact values possesses an exhaust...

On δ-continuous selections of small multifunctions and covering properties

The spaces for which each δ-continuous function can be extended to a 2δ-small point-open l.s.c. multifunction (resp. point-closed u.s.c. multifunction) are studied. Some sufficient conditions and counterexamples are given.

Extremal Selections of Multifunctions Generating a Continuous Flow

n be a continuous multifunction with compact, not necessarily convex values. If F is Lipschitz continuous, it was shown in [4] that there exists a measurable selection f of F such that, for every x 0 , the Cauchy problem ˙ x(t) = f (t, x(t)), x(0) = x 0 has a unique Caratheodory solution, depending continuously on x 0. In this paper, we prove that the above selection f can be chosen so that f (...

Two Results about Fixed Point of Multifunctions