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Dimensions of new fractal functions and associated measures

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Abstract

In this paper, we obtain a vector-valued fractal interpolation function in a more general setting by using the Rakotch fixed point theory and the iterated function system. We also show the existence of the Borel probability measure, widely known as a fractal measure, supported on the graph of this vector-valued fractal interpolation function. We obtain the Hausdorff dimension and the box-counting dimension of the graph of this more general fractal function using some function spaces. We obtain bounds for the fractal dimension of the graph of the Riemann-Liouville fractional integral of this fractal function. Using our techniques, we also calculate the fractal dimensions of the graphs of some fractal interpolation functions.

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Acknowledgements

We would like to thank the anonymous referees for their valuable comments and suggestions that substantially improved the presentation of this paper.

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The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

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  1. Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, 110016, India

    Manuj Verma & Amit Priyadarshi

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  1. Manuj Verma
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Correspondence to Amit Priyadarshi.

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Verma, M., Priyadarshi, A. Dimensions of new fractal functions and associated measures. Numer Algor 94, 817–846 (2023). https://doi.org/10.1007/s11075-023-01521-0

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Mathematics Subject Classification (2010)