## Saturated contraction principles for non self operators, generalizations and applications.(English)Zbl 1478.54047

Summary: Let $$(X, d)$$ be a metric space, $$Y \subset X$$ a nonempty closed subset of $$X$$ and let $$f : Y \to X$$ be a non self operator. In this paper we study the following problem: under which conditions on $$f$$ we have all of the following assertions:
1.
The operator $$f$$ has a unique fixed point;
2.
The operator $$f$$ satisfies a retraction-displacement condition;
3.
The fixed point problem for $$f$$ is well posed;
4.
The operator $$f$$ has the Ostrowski property.
Some applications and open problems related to these questions are also presented.

### MSC:

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