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Quantum Bernstein Fractal Functions
Vijender N., A. Navascués M., V. Sebastián M.
Published in Wiley
2020
Abstract

In this article, taking the quantum Bernstein functions as base functions, we have proposed the class of quantum Bernstein fractal functions. When $f ∈ 𝒞 ( I ) ,$the base function is taken as the classical q-Bernstein polynomials, we propose the class of quantum fractal functions through a multivalued quantum fractal operator. When $f ∈ ℒ p ( I ) , 1 ≤ p ≤ ∞ ,$the base function is assumed as q-Kantorovich-Bernstein polynomial to construct the sequence of $( q , α )$-Kantorovich-Bernstein fractal functions that converges uniformly to f. Some approximation properties of these new class of quantum fractal interpolants have been studied.