Sentence examples for mappings with closed from inspiring English sources

Our analysis is based on the fact that fuzzy fixed point results can be obtained from the fixed point theorem of multivalued mappings with closed values.

By employing the Leray-Schauder alternative, they gave more general existence theorems for ICP ( f, g, K ) and SICP ( f, g, K ) when f, g are set-valued lower semicontinuous mappings with closed convex values.

Since S1 and S2 are upper semicontinuous set-valued mappings with nonempty closed values, it follows from Lemma 2.1 that S1 and S2 are closed mappings.

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

Let be a sequence of nonexpansive mappings with on a closed convex subset of a Banach space and let be a sequence in with (C1). is said to have Browder's property if for each, a sequence defined by (2.10).

The set-valued mappings (S_{i}:X rightarrow2^{X_{i}}) and (T_{i}:Yrightarrow2^{Y_{i}}) are compact closed mappings with nonempty and convex values.

Let be a topological space, with closed and Let be mappings such that for every countable set (3.37).

Let M be a closed subset of an ordered Banach space X with normal order cone, and let (S,Tcolon Mto2^{M}) be two closed (with closed graph) weakly isotone mappings satisfying condition (D_{M}).

Then (Gamma(p):P_{0}rightarrow2^{Xtimes Y}) is u.s.c. the set-valued mappings (S_{i}:X rightarrow2^{X_{i}}) and (T_{i}:Xrightarrow2^{Y_{i}}) are compact closed continuous mappings with nonempty convex values, the vector-valued mappings (f_{i}:Xtimes Ytimes X_{i}rightarrow Z_{i}) and (g_{i}:Xtimes Ytimes Y_{i}rightarrow Z_{i}) are continuous.

Let M be a closed subset of an ordered Banach space X with normal order cone, and let (S,Tcolon Mto2^{M}) be two closed (with closed graph), weakly countably condensing weakly isotone mappings.

Let be a nonempty, closed, and convex subset of a uniformly convex and uniformly smooth Banach space and a closed quasi- -nonexpansive mappings with a fixed point.