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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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