Quantum Bernstein fractal functions. Issue 3 (16th September 2020) - Vijender, N.; Chand, A.K.B.; Navascués, M. A.; Sebastián, M. V.
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.