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Revisiting Ćirić–Reich–Rus type iterated function systems

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Abstract

Using the Hutchinson–Barnsley approach, we provide another way to proving that a Ćirić–Reich–Rus type iterated function system (IFS) has a unique attractor than that taken by Miculescu and Mihail (J Fixed Point Theory Appl 18(2), 285–296, 2016).

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Abbreviations

\(\mathbb {N}_N\) :

The set of first N positive integers

\(\vee ,\bigvee \) :

\(\max \); \(\wedge \) := Finite index set

\((\mathcal {K},\rho )\) :

Metric space; \(\omega ,\upsilon \in \mathcal {K}\); \(P:(\mathcal {K},\rho )\rightarrow (\mathcal {K},\rho )\)

\(F_S\) :

\(\{\theta \in \mathcal {K}~|~P\theta =\theta \}\), \(\mathcal {K}_S\) := \(\mathcal {K}-F_S\)

\(\mathcal {H}(\mathcal {K})\) :

The set of all nonempty compact subsets of \(\mathcal {K}\)

\(\theta \in \Theta \in \mathcal {H}(\mathcal {K})\) :

\(P_H\Theta := {\bigcup ~\{P\theta \}} P_{H,k}\Theta := \underset{k\in \wedge }{\bigcup }\{P_k\theta \}\)

\((\mathcal {H}(\mathcal {K}),\sigma (\rho ))\) :

Hausdorff metric space

IFS:

Iterated function system

HB:

Hutchinson–Barnsley

CRR:

Ćirić–Reich–Rus

GP:

Generalized Picard

HR:

Hardy–Rogers

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Acknowledgements

It is the authors’ sincere gratitude to editor Prof. Pasquale Vetro and the referee(s) for their careful review and suggestions for improvement. S. K. Katiyar acknowledges the financial support received from Dr. B. R. Ambedkar National Institute of Technology (NIT), Jalandhar, Punjab - 144011, India (Institute seed grant).

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Authors and Affiliations

  1. Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Chennai, Tamil Nadu, 603203, India

    B. V. Prithvi

  2. Department of Mathematics, Dr. B. R. Ambedkar National Institute of Technology (NIT), Jalandhar, Punjab, 144011, India

    S. K. Katiyar

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  1. B. V. Prithvi
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Prithvi, B.V., Katiyar, S.K. Revisiting Ćirić–Reich–Rus type iterated function systems. Rend. Circ. Mat. Palermo, II. Ser (2024). https://doi.org/10.1007/s12215-024-01005-7

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