# Journal of Advances in Applied Mathematics

### Lebesgue Function for Higher Order Hermite-Fej´er Interpolation Polynomials with Exponential-Type Weights

Download PDF (199.5 KB) PP. 146 - 158 Pub. Date: October 6, 2020

### Author(s)

**Ryozi SAKAI**^{*}

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

### Abstract

### Keywords

### References

[1] 1. H. S. Jung and R. Sakai, Orthonormal polynomials with exponential-type weights, J. Approx. Theory 152(2008) 215-238.

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

[3] 3. H. S. Jung and R. Sakai, Markov-Bernstein inequality and Hermite-Fej′er interpolation for exponential-type weights, J. Approx. Theory 162(2010), 1381-1397.

[4] 4. H. S. Jung and R. Sakai, Higher order derivatives of approximation polynomials on R, Journal of Inequalities and Applications (2015), 2015:268.DOI 10.1186/513660-015-0789-y.

[5] 5. H. S. Jung, G. Nakamura, R. Sakai and N. Suzuki, Convergence and Divergence of Higher-Order Hermite or Hermite-Fej¨er Interpolation Polynomials with Exponential-Type Weights, ISRN Mathematical Analysis, Volume 2012, ArticleID 904169, 31 pages, doi:10.5042/2012/904169.

[6] 6. A. L. Levin and D. S. Lubinsky, Orthogonal polynomials for exponential weights, Springer, New York, 2001.

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

[8] 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 (2013) 83-101.

[9] 9. R. Sakai, Lp-Convergence of Orthogonal Polynomial Expansions for Exponential Weights, Journal of Advances in Applied Mathematics, Vol.5, No.3, July 2020, https;//dx.doi.org/10.22606/jaam.2020.53001.