Sentence examples for maps in complete from inspiring English sources

Nadler [1] extended Banach's fixed point theorem [2] for set-valued maps in complete metric spaces.

By using these results, we can obtain some generalizations of Kannan's fixed point theorem and Chatterjea's fixed point theorem for nonlinear multivalued contractive maps in complete metric spaces.

Recall that the investigations of fixed points of maps in complete generalized metric spaces appeared for the first time in Diaz and Margolis [8] and Margolis [9].

Also without considering lower semi-continuity, he proved fixed point theorem for set-valued maps in complete generating spaces of a quasi-metric family.

In this paper, we first present a fixed point theorem for set-valued fuzzy contraction type maps in complete fuzzy metric spaces which extends and improves some well-know results in literature.

Recently, Samet and Vetro [20] generalized the notion of coupled fixed points to fixed points of N-order and proved existence results for single maps in complete metric spaces.

We also obtain a fixed point result for self-maps in complete metric spaces satisfying a contractive condition.

In this note, we give new short proofs of Du-Karapinar-Shahzad's intersection theorems for multivalued non-self-maps in complete metric spaces.

Recently, Samet et al. [34] introduced the notions of α - ψ -contractive and α -admissible mapping in complete metric spaces.

A necessary condition for a self-mapping in complete metric space to be an times reasonable expansive self-mapping which satisfies Property  (3.20) is that (3.23) holds.

In this paper some new fixed point theorems for nonlinear contractive type and nonlinear compatible type mapping in complete Menger probabilistic metric spaces are proved.