Sentence examples for maps with nonempty from inspiring English sources

where, are set-valued maps with nonempty values.

Consider the following: and are upper semicontinuous and convex set-valued maps with nonempty convex compact values.

Finally, a variety of fixed point theorems for multi-valued maps with nonempty and convex values is available to conclude the existence of a solution.

In the second result, we shall combine the nonlinear alternative of Leray-Schauder type for single-valued maps with a selection theorem due to Bressan and Colombo for lower semicontinuous multivalued maps with nonempty closed and decomposable values.

(1.1) Here, (H_{i} : [0,1]times[0,1] times E_{1}timescdotstimes E_{N} to E_{i}) are multivalued maps with nonempty values and (E_{i}) are Banach spaces.

The first result relies on a nonlinear alternative for contractive maps, while in the second result, we shall combine the nonlinear alternative of Leray-Schauder type for single-valued maps with a selection theorem due to Bressan and Colombo for lower semi-continuous multivalued maps with nonempty closed and decomposable values.

Let be a set valued mapping with nonempty closed convex values, and be the mappings.

multivalued map with nonempty compact values.

map with nonempty closed -convex values.

mapping with (nonempty) compact and convex values.

is an upper semicontinuous map with nonempty compact values.