## 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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