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Advances in Applied Clifford Algebras

, Volume 22, Issue 2, pp 313–319 | Cite as

Approximation by Quaternion q-Bernstein Polynomials, q > 1

  • Sorin G. Gal
Article

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.

Keywords

Quaternion q-Bernstein-polynomials of quaternion variable order of approximation analytic functions in Weierstrass sense 

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References

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of OradeaOradeaRomania

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