Approximation by Hidden Variable Fractal Functions: A Sequential Approach
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The hidden variable fractal approximation is more diverse than classical fractal approximation. The main goal of the article is to establish new kind of hidden variable fractal approximants which possess convergence and non-differentiability simultaneously for any choice of the scaling factors. Without imposing any condition on the scaling vector, we establish the constrained approximation by the proposed hidden variable fractal approximants. By imposing suitable conditions on the scaling factors, we study the calculus of proposed hidden variable fractal approximants. We identify the suitable conditions for the parameters of hidden variable iterated function system so that the proposed hidden variable fractal functions preserve fundamental shape properties such as monotonicity and convexity in addition to the smoothness of the original function in the given compact interval.
KeywordsHidden variable fractal approximation convergence irregularity non-self-referential self-referential constrained fractal approximation
Mathematics Subject Classification28A80 41A17 41A30
The author is grateful to the referees for extensive comments and constructive suggestions. The valuable comments and suggestions led to several improvements in the paper. The author acknowledges the financial support received from Council of Scientific & Industrial Research (CSIR), India (Project No. 25(0290)/18/EMR-II).
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