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Fixed point theorems for set-valued Y-contractions

Ioan A. Rus, Adrian Petruşel, Gabriela Petruşel (2007)

Banach Center Publications

The purpose of this paper is to present several fixed point theorems for the so-called set-valued Y-contractions. Set-valued Y-contractions in ordered metric spaces, set-valued graphic contractions, set-valued contractions outside a bounded set and set-valued operators on a metric space with cyclic representations are considered.

Fixed point theorems of G -fuzzy contractions in fuzzy metric spaces endowed with a graph

Satish Shukla (2014)

Communications in Mathematics

Let ( X , M , * ) be a fuzzy metric space endowed with a graph G such that the set V ( G ) of vertices of G coincides with X . Then we define a G -fuzzy contraction on X and prove some results concerning the existence and uniqueness of fixed point for such mappings. As a consequence of the main results we derive some extensions of known results from metric into fuzzy metric spaces. Some examples are given which illustrate the results.

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