Sentence examples for maps with convex from inspiring English sources

maps with convex, compact values with the same properties (see e.g. Chapter I.3.3 in [14]).

convex set-valued maps with convex compact values, and for any,, and, we have,,, and Therefore, (4.2).

Corollary 7.2, the Marchaud maps F can be replaced by more general upper Carathéodory maps with convex, compact values.

Since Michael [1] constructed continuous ϵ-approximate selections for the lower semicontinuous maps with convex values in Banach spaces, the result has been improved in many ways.

It was extended to lower semicontinuous maps with convex values except on a set of topological dimension less than or equal to zero by Michael and Pixley [2] in 1980.

set-valued mapping with convex and compact values.

Thus, by Proposition 1, (mathcal{N}) is an upper semi-continuous compact map with convex closed values.

Let E be a Banach space and y ∈ E. Let f : E → R ∪ be a proper, convex and lower semi-continuous mapping with convex domain D ( f ).

Let, and let be defined by for Then is an u.s.c. and convex set-valued map with convex compact values, and for each, and,.

Let E be a Banach space and let f : E → R ∪ be a proper, convex and lower semicontinuous mapping with convex domain D ( f ).

(16) In the sense of Step 1, (mathcal{N}_{1}) is an upper semi-continuous compact map with convex closed values.