Fixed Point Theory in Graph Metric Spaces

A. Petruşel () and G. Petruşel ()
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A. Petruşel: Department of Mathematics
G. Petruşel: Department of Business

A chapter in Approximation and Computation in Science and Engineering, 2022, pp 679-691 from Springer

Abstract: 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.

Keywords: Metric space; Directed graph; G-contraction; Generalized contraction; Increasing operator; Decreasing operator; Generalized G-monotone operator; Fixed point; (Weakly) Picard operator; Stability; Gronwall lemma; Open problem; 47H10; 34G20; 45N05; 06A06; 47H09; 47H07; 54E35; 54H25 (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-84122-5_37

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DOI: 10.1007/978-3-030-84122-5_37

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