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Convergence and Divergence of Higher-Order Hermite or Hermite-Fejér Interpolation Polynomials with Exponential-Type Weights
- Source :
- ISRN Mathematical Analysis. 2012:1-31
- Publication Year :
- 2012
- Publisher :
- Hindawi Limited, 2012.
-
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 2 𝜌 ; 𝑥 ) of degree 𝑛 for 𝑤 2 𝜌 ( 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 } 𝑛 𝑘 = 1 of 𝑝 𝑛 ( 𝑤 2 𝜌 ; 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 } 𝑛 𝑘 = 1 of 𝑝 𝑛 ( 𝑤 2 𝜌 ; 𝑥 ) .
Details
- ISSN :
- 20904665
- Volume :
- 2012
- Database :
- OpenAIRE
- Journal :
- ISRN Mathematical Analysis
- Accession number :
- edsair.doi.dedup.....63b0c9798c5fb7369bcf50738ef6c528