Convergence and Divergence of Higher-Order Hermite or Hermite-Fejér Interpolation Polynomials with Exponential-Type Weights. (16th May 2012)

• Record Type: Journal Article
• Authors: Jung, Hee Sun; Nakamura, Gou; Sakai, Ryozi; Suzuki, Noriaki
• Other Names: Ricceri B. Academic Editor.; Yu W. Academic Editor.
• Is Part Of: ISRN mathematical analysis. Volume 2012(2012)
• Publication Date: 2012-05-16
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Periodicals; 515
• DOI: 10.5402/2012/904169
• Languages: English
• ISSNs: 2090-4657

Abstract

Abstract : Let R = ( - ∞, ∞ ), and let w ρ ( x ) = | x | ρ e - Q ( x ), where ρ > - 1 / 2 and Q ∈ C 1 ( R ) : R → R + = [ 0, ∞ ) is an even function. Then we can construct the orthonormal polynomials p n ( w ρ 2 ; x ) of degree n for w ρ 2 ( x ) . In this paper for an even integer ν ≥ 2 we investigate the convergence theorems with respect to the higher-order Hermite and Hermite-Fejér interpolation polynomials and related approximation process based at the zeros { x k, n, ρ } k = 1 n of p n ( w ρ 2 ; x ) . Moreover, for an odd integer ν ≥ 1, we give a certain divergence theorem with respect to the higher-order Hermite-Fejér interpolation polynomials based at the zeros { x k, n, ρ } k = 1 n of p n ( w ρ 2 ; x ) .