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Fractal Dimension of \(\alpha \)-Fractal Functions Without Endpoint Conditions

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Abstract

In this article, we manifest the existence of a new class of \(\alpha \)-fractal functions without endpoint conditions in the space of continuous functions. Furthermore, we add the existence of the same class in numerous spaces such as the Hölder space, the convex Lipschitz space, and the oscillation space. We also estimate the fractal dimensions of the graphs of the newly constructed \(\alpha \)-fractal functions adopting some function spaces and covering methods.

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Acknowledgements

The authors would like to thank the referees for reviewing the manuscript and providing their constructive comments and suggestions to improve the manuscript. The first author acknowledges the Prime Minister’s Research Fellowship (PMRF) from the Ministry of Education, Government of India (PMRF ID: 2202749) for the financial support for his Ph.D. work.

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Authors and Affiliations

  1. Department of Mathematics, IIT Jodhpur, Jodhpur, 342037, India

    Gurubachan & V. V. M. S. Chandramouli

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

    S. Verma

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  1. Gurubachan
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  2. V. V. M. S. Chandramouli
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  3. S. Verma
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Correspondence to S. Verma.

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Gurubachan, Chandramouli, V.V.M.S. & Verma, S. Fractal Dimension of \(\alpha \)-Fractal Functions Without Endpoint Conditions. Mediterr. J. Math. 21, 71 (2024). https://doi.org/10.1007/s00009-024-02610-7

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  • DOI: https://doi.org/10.1007/s00009-024-02610-7

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