Selections Of Set-valued Mappings Research Articles

On Continuous Selections of Set-valued Mappings with Almost Convex Values

In this paper, it is proved that through each point of the graph of a continuous setvalued mapping with almost convex and star-like values can be passed a continuous selection of that mapping.

On directional derivatives of selections of set-valued mappings

The paper is devoted to the question of existence of directional derivatives of selections of some set-valued mappings with starlike graphs.

On Selections of Set-Valued Maps Satisfying Some Inclusions in a Single Variable

Abstract We present the results on the stability of some set-valued functional equations with applications to the gamma-type equations or linear equations.

Paracompactness, Selections and Factorization Principles

Factorization principles for set-valued mappings are obtained. These principles are applied in theorems for selections of set-valued mappings from paracompact spaces.

Selections of set-valued mappings with hereditarily collectionwise normal domain

It is shown that every l.s.c. closed-and-convex valued mapping Φ :X→2 Y , where X is a hereditarily collectionwise normal and countably paracompact space and Y is a reflexive Banach space has a single-valued continuous selection.

Extensions of l.s.c. Mappings into Reflexive Banach Spaces

Every lower semi-continuous closed-and-convex valued mapping Φ: X→2Y where X is a collectionwise normal and countably paracompact space and Y is a reflexive Banach space can be extended to the Dieudonne completion μ(X) of X. Generalizations and applications to the theory of selections of set-valued mappings are presented.

Monomial selections of set-valued maps

The main result of this paper offers a necessary and sufficient condition for the existence of a multimonomial selection of a set-valued map with weakly compact convex values defined on an amenable semigroup.