# Journal of Advances in Applied Mathematics

### A Study of Weighted Polynomial Approximations for Orthogonal Polynomial Expansion

Download PDF (642.7 KB) PP. 173 - 195 Pub. Date: July 31, 2017

### Author(s)

**Ryozi Sakai**^{*}

Department of Mathematics, Meijo University, Tenpaku-ku, Nagoya 468-8502, Japan

### Abstract

### Keywords

### References

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*p*≤ ∞), Journal of Approximation Theory 94(1998), 333-382.

[2] H. S. Jung and R. Sakai, Higher order derivatives of approximation polynomial on R, Journal of inequalities and applications, 2015: 268, DOI 10.1186/s13660-o15-0789-y.

[3] D. S. Lubinsky, A Survey of Weighted Polynomial Approximation with Exponential Weights, Surveys on Approximation Theory, 3(2007), 1-105.

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

[5] H. N. Mhaskar, Extensions of the Dirichlet?Jordan Convergence Criterion to a General Class of Orthogonal Polynomial Expansions, Journal of Approximation Theory 42 (1984), 138-148.

[6] W. Rudin, Principles of Mathematical Analysis, McGraw-Hill, New York, 1964.

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

[8] 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, pp.83-101, 2013.

[9] K. Itoh, R. Sakai and N. Suzuki, The de la Vall′ee Poussin Mean and Polynomial Appoximation for Exponential Weight, International Journal of Analysis, 2015, Article ID 706930, 8 pages, (2015).

[10] K. Itoh, R. Sakai and N. Suzuki, An estimate for derivative of the de la Vall′ee Poussin mean, Math. J. Ibaraki Univ. 47 (2015), 1-18.

[11] K. Itoh, R. Sakai and N. Suzuki, Uniform convergence of orthogonal polynomial expansions for exponential weights, preprint.

[12] K. Itoh, R. Sakai and N. Suzuki, Polynomial approximation for absolutely continuous functions, accepted by Tohoku Math. Journal.