Sentence examples for mappings with nonempty from inspiring English sources

The next result concerns weak G-contraction multivalued mappings with nonempty closed values.

For each i ∈ {1, 2}, let S i : K × K → 2 K be continuous set-valued mappings with nonempty compact convex values and T i : K × K → 2 D be upper semicontinuous set-valued mappings with nonempty compact convex values.

Let S : K → 2 K be continuous set-valued mappings with nonempty compact convex values and T : K → 2 D be upper semicontinuous set-valued mappings with nonempty compact convex values.

Let S1, S2 : K → 2 K be continuous set-valued mappings with nonempty compact convex values and T1, T2 : K → 2 D be upper semicontinuous set-valued mappings with nonempty compact convex values.

Then, it is easy to see that H and G are upper semicontinuous mappings with nonempty closed convex values.

Let be a compact locally -convex space and an upper semicontinuous set-valued mappings with nonempty closed acyclic values.

We observe that Theorem 2 can be investigated for a characterization of Lipschitzian mappings T with nonempty fixed point sets (operatorname{Fix}(T)).   3.

We observe that Theorem 2 can be investigated for a characterization of Lipschitzian mappings T with nonempty fixed point sets (operatorname{Fix}(T)).

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

Let be a mapping with nonempty -convex values, and let and be mappings and be a mapping such that, for each, is a closed, pointed, and convex cone in with.

Let be strictly pseudocontractive mappings with being nonempty.