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Search Results: 1 - 10 of 1248 matches for " Ryozi Sakai "
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A Study of Weighted Polynomial Approximations with Several Variables (II)  [PDF]
Ryozi Sakai
Applied Mathematics (AM) , 2017, DOI: 10.4236/am.2017.89093
Abstract: In this paper we investigate weighted polynomial approximations with several variables. Our study relates to the approximation for \"\" by weighted polynomial. Then we will give some results relating to the Lagrange interpolation, the best approximation, the Markov-Bernstein inequality and the Nikolskii- type inequality.
A Study of Weighted Polynomial Approximations with Several Variables (I)  [PDF]
Ryozi Sakai
Applied Mathematics (AM) , 2017, DOI: 10.4236/am.2017.89095
Abstract: In this paper, we investigate the weighted polynomial approximations with several variables. Our study relates to the approximation for \"\" by weighted polynomials. Then we will estimate the degree of approximation.
Some Properties of Orthogonal Polynomials for Laguerre-Type Weights
HeeSun Jung,Ryozi Sakai
Journal of Inequalities and Applications , 2011, DOI: 10.1155/2011/372874
Abstract:
Derivatives of Integrating Functions for Orthonormal Polynomials with Exponential-Type Weights
Jung HeeSun,Sakai Ryozi
Journal of Inequalities and Applications , 2009,
Abstract: Let , , where is an even function. In 2008 we have a relation of the orthonormal polynomial with respect to the weight ; , where and are some integrating functions for orthonormal polynomials . In this paper, we get estimates of the higher derivatives of and , which are important for estimates of the higher derivatives of .
Some Properties of Orthogonal Polynomials for Laguerre-Type Weights
Jung HeeSun,Sakai Ryozi
Journal of Inequalities and Applications , 2011,
Abstract: Let , let be a continuous, nonnegative, and increasing function, and let be the orthonormal polynomials with the weight . For the zeros of we estimate , where is a positive integer. Moreover, we investigate the various weighted -norms ( ) of .
Approximation by Lupas-Type Operators and Szász-Mirakyan-Type Operators
Hee Sun Jung,Ryozi Sakai
Journal of Applied Mathematics , 2012, DOI: 10.1155/2012/546784
Abstract: Lupas-type operators and Szász-Mirakyan-type operators are the modifications of Bernstein polynomials to infinite intervals. In this paper, we investigate the convergence of Lupas-type operators and Szász-Mirakyan-type operators on [0,∞).
Asymptotic Properties of Derivatives of the Stieltjes Polynomials
Hee Sun Jung,Ryozi Sakai
Journal of Applied Mathematics , 2012, DOI: 10.1155/2012/482935
Abstract: Let ()∶=(1?2)?1/2 and ,() be the ultraspherical polynomials with respect to (). Then, we denote the Stieltjes polynomials with respect to () by ,
Derivatives of Integrating Functions for Orthonormal Polynomials with Exponential-Type Weights
Hee Sun Jung,Ryozi Sakai
Journal of Inequalities and Applications , 2009, DOI: 10.1155/2009/528454
Abstract: Let wρ(x):=|x|ρexp( Q(x)), ρ> 1/2, where Q∈C2:( ∞,∞)→[0,∞) is an even function. In 2008 we have a relation of the orthonormal polynomial pn(wρ2;x) with respect to the weight wρ2(x); pn′(x)=An(x)pn 1(x) Bn(x)pn(x) 2ρnpn(x)/x, where An(x) and Bn(x) are some integrating functions for orthonormal polynomials pn(wρ2;x). In this paper, we get estimates of the higher derivatives of An(x) and Bn(x), which are important for estimates of the higher derivatives of pn(wρ2;x).
Pointwise Convergence of Fourier-type Series with Exponential Weights
Hee Sun Jung,Ryozi Sakai
Mathematics , 2014,
Abstract: Let $\mathbb{R}=(-\infty,\infty)$, and let $Q\in C^1(\mathbb{R}): \mathbb{R}\rightarrow[0,\infty)$ be an even function. We consider the exponential weights $w(x)=e^{-Q(x)}$, $x\in \mathbb{R}$. In this paper we obtain a pointwise convergence theorem for the Fourier-type series with respect to the orthonormal polynomials $\left\{p_n(w^2;x)\right\}$.
$L_p$-Convergence of higher order Hermite or Hermite-Fejér interpolation polynomials with exponential-type weights
Hee Sun Jung,Ryozi Sakai
Mathematics , 2014,
Abstract: Let $\mathbb{R}=(-\infty,\infty)$, and let $Q\in C^1(\mathbb{R}): \mathbb{R}\rightarrow \mathbb{R^+}=[0,\infty)$ be an even function, which is an exponent. We consider the weight $w_\rho(x)=|x|^{\rho} e^{-Q(x)}$, $\rho\geqslant 0$, $x\in \mathbb{R}$, and then we can construct the orthonormal polynomials $p_{n}(w_\rho ^2;x)$ of degree n for $w_\rho ^2(x)$. In this paper we obtain $L_p$-convergence theorems of even order Hermite-Fej\'er interpolation polynomials at the zeros $\left\{x_{k,n,\rho}\right\}_{k=1}^n$ of $p_{n}(w_\rho ^2;x)$.
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