The Degree of Approximation and Converse Theorems with Exponential-Type Weights

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DOI: 10.22606/jaam.2018.31001

Author(s)

Ryozi SAKAI^*
Department of Mathematics, Meijo University, Tenpaku-ku Nagoya 468-8502, Japan

Abstract

Keywords

exponential-type weights, degree of approximation, Nikolskii-type inequalities

References

[1] H. N. Mhaskar, “Introduction to the Theory of Weighted Polynomial Approximation,” World Scientific, Singapore, 1996.

[2] G. G. Lorentz, “Approximation of Functions”, Holt, Rinehart and Winston, 1966.

[3] S. B. Damelin, “Converse and Smoothness Theorems for Erd¨os Weights in Lp (0 < p 6 ∞),”Journal of Approximation Theory 93 (1998), 349-398.

[4] S. B. Damelin and D. S. Lubinsky, “Jackson Theorems for Erd¨os Weights in Lp (0 < p 6 ∞),”Journal of Approximation Theory 94 (1998), 333-382.

[5] A. L. Levin and D. S. Lubinsky, "Orthogonal Polynomials for Exponential Weights," Springer, New York, 2001.

[6] H. S. Jung and R. Sakai, "Specific examples of exponential weights, Commun." Korean Math. Soc. 24 (2009), No.2, 303-319.

[7] R. Sakai and N. Suzuki, "Mollification of exponential weights and its application to the Markov-Bernstein inequality," Pioneer J. of Math., Vol.7, no.1 (2013) 83-101.

[8] R. Sakai and N. Suzuki, "Favard-type inequalities for exponential weights," Pioneer J. of Math. vol 3. No.1 (2011), 1-16.

Journal of Advances in Applied Mathematics