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Concerning the Vector-Valued Fractal Interpolation Functions on the Sierpiński Gasket

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Abstract

The present paper is concerned with the study of vector-valued interpolation functions on the Sierpiński gasket by certain classes of fractal functions. This extends the known results on the real-valued and vector-valued fractal interpolation functions on a compact interval in \({\mathbb {R}}\) and the real-valued fractal interpolation on the Sierpiński gasket. We study the smoothness property of the vector-valued fractal interpolants on the Sierpiński gasket. A few elementary properties of the fractal approximants and the fractal operator that emerge in connection with the vector-valued fractal interpolation on the Sierpiński gasket are indicated. Some constrained approximation aspects of the vector-valued fractal interpolation function on the Sierpiński gasket are pointed out.

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Acknowledgements

The second author thanks the University Grants Commission (UGC), India, for financial support in the form of a Senior Research Fellowship.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Escuela de Ingeniería y Arquitectura, Universidad de Zaragoza, Zaragoza, Spain

    M. A. Navascués

  2. Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, India

    S. Verma & P. Viswanathan

  3. Department of Applied Sciences, IIIT Allahabad, Prayagraj, 211015, India

    S. Verma

Authors
  1. M. A. Navascués
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  2. S. Verma
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  3. P. Viswanathan
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Correspondence to S. Verma.

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Navascués, M.A., Verma, S. & Viswanathan, P. Concerning the Vector-Valued Fractal Interpolation Functions on the Sierpiński Gasket. Mediterr. J. Math. 18, 202 (2021). https://doi.org/10.1007/s00009-021-01847-w

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  • DOI: https://doi.org/10.1007/s00009-021-01847-w

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