Sentence examples for mappings and multivalued from inspiring English sources

We discuss the existence of common fixed points in uniformly convex metric spaces for single-valued pointwise asymptotically nonexpansive or nonexpansive mappings and multivalued nonexpansive, -nonexpansive, or -semicontinuous maps under different conditions of commutativity.

Summarizing, in this paper we prove some common fixed point results either in uniformly convex metric space with the FPPMM (Section 3) or -trees (Section 4) for single-valued asymptotic pointwise nonexpansive or nonexpansive mappings and multivalued nonexpansive, -nonexpansive, or -semicontinuous maps which improve and/or complement Theorem DKP, [17, Theorem  3.3], and many others.

Analogous coincidence theorems for fuzzy mappings and multivalued mappings have been obtained as corollaries.

Since then, many authors studied the problem of existence of fixed points for single-valued mappings and multivalued mappings in several spaces with graphs; see [19 23].

We consider the equivalence of the existence of fixed points of single-valued mappings and multivalued mappings for some classes of mappings by proving some equivalence theorems for the completeness of metric spaces.

These corollaries regarding coincidence point of fuzzy mappings and multivalued mappings have not been seen in the literature and therefore most of them are still original and new results.

Now we introduce a new iteration method for a family of single-valued nonexpansive mappings and a multivalued nonexpansive mapping.

Many interesting fixed point results for contraction mappings for singlevalued and multivalued mappings in probabilistic metric spaces can be found in [8].

Naturally, many authors have started to investigate the existence of a fixed point theorem via α-admissible mappings for single valued and multivalued mappings (see [31 38]).

The Banach contraction principle has been extended in different directions either by using generalized contractions for multivalued mappings and hybrid pairs of single and multivalued mappings, or by using more general spaces.

In this section, we establish Theorem 5 on the existence of an α-fuzzy fixed point of a fuzzy mapping and also obtain a fixed point of fuzzy mappings (see Corollaries 8 and 9) and multivalued mappings (see Corollary 7).