Approximation Theory, Tampa pp 70-82 | Cite as

# Some examples in approximation on the unit disk by reciprocals of polynomials

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## Abstract

This paper is a continuation of the authors’ study of approximation by reciprocals of polynomials. A Jackson-type theorem for such approximants is established for a certain class of functions f analytic and nonzero in the disk |z|<1 and continuous on |z|≤1. Furthermore, we obtain the sharp degree of convergence for reciprocal polynomial approximation on |z|≤1 to functions f that are analytic on |z|≤1, nonzero in |z|<1, and vanish somewhere on |z|=1.

## AMS subject classification 41A20

41A17## Preview

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## References

- 1.Levin A.L. and Saff E.B., Degree of approximation of real functions by reciprocals of real and complex polynomials, SIAM J. Math. Analysis (to appear).Google Scholar
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**38**(1934), 163–176.CrossRefMathSciNetGoogle Scholar

## Copyright information

© Springer-Verlag 1987