Convergence and Divergence of Higher-Order Hermite or Hermite-Fejér Interpolation Polynomials with Exponential-Type Weights-Reference-Cited by-同舟云学术

Convergence and Divergence of Higher-Order Hermite or Hermite-Fejér Interpolation Polynomials with Exponential-Type Weights

Published:2012-05-16 Issue: Volume:2012 Page:1-31
ISSN:2090-4665
Container-title:ISRN Mathematical Analysis
language:en
Short-container-title:ISRN Mathematical Analysis

Author:

Jung Hee Sun¹,Nakamura Gou²,Sakai Ryozi³,Suzuki Noriaki³^ORCID

Affiliation:

1. Department of Mathematics Education, Sungkyunkwan University, Seoul 110-745, Republic of Korea

2. Science Division, Center for General Education, Aichi Institute of Technology, Yakusa-cho, Toyota 470-0392, Japan

3. Department of Mathematics, Meijo University, Nagoya 468-8502, Japan

Abstract

Let and let , where and is an even function. Then we can construct the orthonormal polynomials of degree for . In this paper for an even integer 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 of . Moreover, for an odd integer , we give a certain divergence theorem with respect to the higher-order Hermite-Fejér interpolation polynomials based at the zeros of .

Publisher

Hindawi Limited

Subject

General Medicine

Link

http://downloads.hindawi.com/archive/2012/904169.pdf

Reference22 articles.

1. Pointwise convergence of Hermite-Fejér interpolation of higher order for Freud weights

2. Convergence of the Derivatives of Hermite-Fejér Interpolation Polynomials of Higher Order Based at the Zeros of Freud Polynomials

3. Hermite and Hermite-Fejér interpolation and associated product integration rules on the real line: The L∞ theory

4. Uniform or Mean Convergence of Hermite–Fejér Interpolation of Higher Order for Freud Weights

5. Orthonormal polynomials with generalized Freud-type weights