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Prithvi, B. V.; Katiyar, S. K.

Comments on “Fractal set of generalized countable partial iterated function system with generalized contractions via partial Hausdorff metric”. (English) Zbl 07792359

Topology Appl. 341, Article ID 108687, 11 p. (2024).
Summary: The purpose of this work is to fill a gap in the article Priya and Uthayakumar (2022) [13]. To prove fractals (fixed points), the authors of that article tried to connect two independent conceptual domains. This results in their main theorem being wrong and becoming a conjecture. This paper scrutinizes and presents both the concepts above to demonstrate fractals in the settings posed in that article. Using a proper definition, the correct theorem to achieve the purpose of that article is discussed.

Cited in 1 Document

MSC:

28A80 Fractals
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
47H04 Set-valued operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)

Keywords:

contraction; partial metric space; fixed point; Picard operator; iterated function system; fractal
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References:

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