Abstract
Coalescence hidden variable fractal interpolation function (CHFIF) proves more versatile than classical interpolant and fractal interpolation function (FIF). Using rational functions and CHFIF, a general construction of \(\mathbf {A}\)-fractal rational functions is introduced for the first time in the literature. This construction of \(\mathbf {A}\)-fractal rational function also allows us to insert shape parameters for positivity-preserving univariate interpolation. The convergence analysis of the proposed scheme is established. With suitably chosen numerical examples and graphs, the effectiveness of the positivity-preserving interpolation scheme is illustrated.
A. K. B. Chand is grateful to Project No. MTR/2017/000574 of Department of Science and Technology, India.
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Katiyar, S.K., Chand, A.K.B. (2021). \(\mathbf {A}\)-Fractal Rational Functions and Their Positivity Aspects. In: Giri, D., Ho, A.T.S., Ponnusamy, S., Lo, NW. (eds) Proceedings of the Fifth International Conference on Mathematics and Computing. Advances in Intelligent Systems and Computing, vol 1170. Springer, Singapore. https://doi.org/10.1007/978-981-15-5411-7_16
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