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Cyclic iterated function systems

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Abstract

In this paper, we consider some generalization of the Banach contraction principle, namely cyclic contraction and cyclic \(\varphi \)-contraction. For the application to the fractal, we develop new iterated function systems (IFS) consisting of cyclic contractions and cyclic \(\varphi \)-contractions. Further, we discuss about some special properties of the Hutchinson operator associated with the cyclic (c)-comparison IFS.

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Acknowledgements

The authors are grateful to Dr. P. Veeramani for his constructive suggestions to use cyclic contraction in iterated function systems. The second author is thankful to the University of Zaragoza for a short visit during July, 2019 for this joint work. The authors are grateful to the anonymous reviewers for their valuable suggestions to improve the presentation of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Madras, Chennai, 600036, India

    R. Pasupathi & A. K. B. Chand

  2. Departmento de Matemática Aplicada, Escuela de Ingeniería y Arquitectura, Universidad de Zaragoza, 50018, Zaragoza, Spain

    M. A. Navascués

Authors
  1. R. Pasupathi
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  2. A. K. B. Chand
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  3. M. A. Navascués
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Correspondence to A. K. B. Chand.

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The second author acknowledges the financial support received from the project MTR/2017/000574-MATRICS of the Science and Engineering Research Board (SERB), Government of India.

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Pasupathi, R., Chand, A.K.B. & Navascués, M.A. Cyclic iterated function systems. J. Fixed Point Theory Appl. 22, 58 (2020). https://doi.org/10.1007/s11784-020-00790-9

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  • DOI: https://doi.org/10.1007/s11784-020-00790-9

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