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2022 | OriginalPaper | Buchkapitel

Fixed Point Theory in Graph Metric Spaces

verfasst von : A. Petruşel, G. Petruşel

Erschienen in: Approximation and Computation in Science and Engineering

Verlag: Springer International Publishing

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Abstract

Let (X, d) be a metric space, G be a graph associated with X and f : X → X be an operator which satisfies two main assumptions:
(1)
f is generalized G-monotone;
 
(2)
f is a G-contraction with respect to d.
In the above framework, we will present sufficient conditions under which:
(i)
f is a Picard operator;
 
(ii)
the fixed point problem x = f(x), x ∈ X is well-posed in the sense of Reich and Zaslavski;
 
(iii)
the fixed point problem x = f(x), x ∈ X has the Ulam-Hyers stability property;
 
(iv)
f has the Ostrowski stability property;
 
(v)
f satisfies to some Gronwall type inequalities.
 
 
Some open questions are presented.

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Metadaten
Titel
Fixed Point Theory in Graph Metric Spaces
verfasst von
A. Petruşel
G. Petruşel
Copyright-Jahr
2022
DOI
https://doi.org/10.1007/978-3-030-84122-5_37