Sentence examples for mappings with compact from inspiring English sources

multivalued mappings with compact values.

If is a nonexpansive mappings with compact values then has at least one fixed point.

Next we consider two further conditions to guarantee the existence of fixed points for nonexpansive set-valued mappings with compact values in uniformly convex metric spaces.

Also in the reflexive case, since is nearly uniform convex, we can also assure that satisfies the w-FPP for nonexpansive multivalued mappings (with compact convex values) (see, e.g., [26]).

In 1991, Chang and Huang [16, 17] introduced and studied some new classes of complementarity problems and variational inequalities for set-valued mappings with compact values in Hilbert spaces.

Recently, Phon-on et al. [22] introduced a new type of weak G-contraction which is weaker than that of Tiammee and Suantai [21], and they proved some fixed point theorems for this type of mappings with compact values which is a generalization of several known results in a complete metric space endowed with a graph.

Statement 2 is true since the restriction of the mapping z to the (compact) set ({pinoperatorname{int}Delta^{n}: p_{i}geq varepsilon _{2}, iin[n]}) is an upper semicontinuous mapping with compact values, and such mappings transform compact sets into compact sets [6], p.560.6.

It is well known that any upper semicontinuous set-valued mapping with compact acyclic values is admissible, and the composition of two admissible mappings is also admissible; see [14].

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.

Theorem 4.5 Let ( E, d ) be a complete CAT ( 0 ) space, C ⊆ E be a closed locally compact convex set, K be a nonempty compact subset of C, and G, H : C → 2 E be two upper semicontinuous set-valued mappings with nonempty compact values.