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Simulation functions and Boyd-Wong type results. (English) Zbl 1431.54022

Summary: In this paper we give new and much shorter proofs of Boyd-Wong and Meir-Keeler type results. Also, we define a new form of Boyd-Wong type contraction mappings using simulation functions and obtain some sufficient conditions for the existence and uniqueness of a fixed point for such class of mappings in the setting of metric spaces. Also, we present some results regarding the property \(P\) for these well-known types of self-mappings.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
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References:

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