Saturated contraction principles for non self operators, generalizations and applications
V Berinde, Ş Măruşter, IA Rus - Filomat, 2017 - JSTOR
V Berinde, Ş Măruşter, IA Rus
Filomat, 2017•JSTORLet (X, d) be a metric space, Y⊂ X a nonempty closed subset of X and let f: Y→ 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.
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.
Abstract
Let (X, d) be a metric space, Y ⊂ X a nonempty closed subset of X and let f : Y → 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.
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