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Fractal Surfaces Involving Rakotch Contraction For Countable Data Sets

Author

Listed:
  • MANUJ VERMA

    (Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, India 110016, India)

  • AMIT PRIYADARSHI

    (Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, India 110016, India)

Abstract

In this paper, we prove the existence of the bivariate fractal interpolation function using the Rakotch contraction theory and iterated function system for a countable data set. We also give the existence of the invariant Borel probability measure supported on the graph of the bivariate fractal interpolation function. In particular, we highlight that our theory encompasses the bivariate fractal interpolation theory in both finite and countably infinite settings available in literature.

Suggested Citation

  • Manuj Verma & Amit Priyadarshi, 2024. "Fractal Surfaces Involving Rakotch Contraction For Countable Data Sets," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(02), pages 1-12.
    • Handle: RePEc:wsi:fracta:v:32:y:2024:i:02:n:s0218348x24400024
    DOI: 10.1142/S0218348X24400024
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