The role of equivalent metrics in fixed point theory
Keywords
Fixed point theory, topologically equivalent metric, strongly equivalent metric, Picard operator, weakly Picard operator, contraction, generalized contraction, well-posedness, shadowing property, stability, Ulam stability, invariant subsetAbstract
Metrical fixed point theory is accomplished by a wide class of terms: \roster \item"$\bullet$" operators (bounded, Lipschitz, contraction, contractive, nonexpansive, noncontractive, expansive, dilatation, isometry, similarity, Picard, weakly Picard, Bessaga, Janos, Caristi, pseudocontractive, accretive, etc.), \item"$\bullet$" convexity (strict, uniform, hyper, etc.), \item"$\bullet$" deffect of some properties (measure of noncompactness, measure of nonconvexity, minimal displacement, etc.), \item"$\bullet$" data dependence (stability, Ulam stability, well-posedness, shadowing property, etc.), \item"$\bullet$" attractor, \item"$\bullet$" basin of attraction$\ldots$ \endroster The purpose of this paper is to study several properties of these concepts with respect to equivalent metrics.Downloads
Published
2013-04-22
How to Cite
1.
PETRUŞEL, Adrian, RUS, Ioan A. and ŞERBAN, Marcel-Adrain. The role of equivalent metrics in fixed point theory. Topological Methods in Nonlinear Analysis. Online. 22 April 2013. Vol. 41, no. 1, pp. 85 - 112. [Accessed 10 December 2024].
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