Fractal rational functions and their approximation properties

• Autores: P. Viswanathan, A.K.B. Chand
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 185, Nº 1, 2014, págs. 31-50
• Idioma: inglés
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• Resumen

  • This article introduces fractal perturbation of rational functions via á-fractal operator and investigates some approximation theoretic aspects of this new function class, namely, the class of fractal rational functions. Its specific aims are: (i) to define fractal rational functions (ii) to investigate the optimal perturbation to a traditional rational approximant corresponding to a continuous function (iii) to establish the fractal rational function analogues of the celebratedWeierstrass theorem and its generalization, namely, theM¨untz theorem (iv) to prove the existence of a best fractal rational approximant to a continuous function defined on a real compact interval, and to study certain properties of the corresponding best approximation operator. By establishing the existence of fractal rational functions that are copositive with a prescribed continuous function, the current article also attempts to invoke fractal functions to the field of shape preserving approximation.