Abstract
Defining for q > 1 the q-Bernstein polynomials of degree n of a quaternion variable, attached to a function f defined on a ball in the field of quaternions, the order of approximation \({\frac{1} {q^n}}\) is obtained when f is in some classes of analytic functions in the sense of Weierstrass. The result extends that in the case of approximation of analytic functions of a complex variable in disks, by q-Bernstein polynomials of complex variable.
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Gal, S.G. Approximation by Quaternion q-Bernstein Polynomials, q > 1. Adv. Appl. Clifford Algebras 22, 313–319 (2012). https://doi.org/10.1007/s00006-011-0310-8
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DOI: https://doi.org/10.1007/s00006-011-0310-8