Topological Methods in Nonlinear Analysis
- Topol. Methods Nonlinear Anal.
- Volume 41, Number 1 (2013), 85-112.
The role of equivalent metrics in fixed point theory
Metrical fixed point theory is accomplished by a wide class of terms:
$\bullet$ operators (bounded, Lipschitz, contraction, contractive, nonexpansive, noncontractive, expansive, dilatation, isometry, similarity, Picard, weakly Picard, Bessaga, Janos, Caristi, pseudocontractive, accretive, etc.),
$\bullet$ convexity (strict, uniform, hyper, etc.),
$\bullet$ deffect of some properties (measure of noncompactness, measure of nonconvexity, minimal displacement, etc.),
$\bullet$ data dependence (stability, Ulam stability, well-posedness, shadowing property, etc.),
$\bullet$ basin of attraction$\ldots$
The purpose of this paper is to study several properties of these concepts with respect to equivalent metrics.
Topol. Methods Nonlinear Anal., Volume 41, Number 1 (2013), 85-112.
First available in Project Euclid: 21 April 2016
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Petruşel, Adrian; Rus, Ioan A.; Şerban, Marcel-Adrain. The role of equivalent metrics in fixed point theory. Topol. Methods Nonlinear Anal. 41 (2013), no. 1, 85--112. https://projecteuclid.org/euclid.tmna/1461253857