Results 1 to 10 of about 97,509 (152)
Global smoothness preservation and the variation-diminishing property
Journal of Inequalities and Applications, 1999 In the center of our paper are two counterexamples showing the independence of the concepts of global smoothness preservation and variation diminution for sequences of approximation operators.
Gavrea Ioan +4 more
doaj +3 more sources
Global smoothness preservation by multivariate singular integrals [PDF]
Bulletin of the Australian Mathematical Society, 2000 By using various kinds of moduli of smoothness, it is established that the multivariate variants of the well-known singular integrals of Picard, Poisson-Cauchy, Gauss-Weierstrass and their Jackson-type generalisations satisfy the “global smoothness preservation” property. The results are extensions of those proved by the authors for the univariate case.
Anastassiou, George A., Gal, Sorin G.
openaire +3 more sources
On global smoothness preservation in complex approximation [PDF]
Annales Polonici Mathematici, 2002 For a function \(f:\mathbb R^m\to\mathbb R\), set \(\Delta_h^rf(x)=\sum_{i=0}^r(-1)^{r-i}\binom{r}{i} f(x+rh)\), and define the \(r\)th \(L^s\)-modulus of smoothness over \(\mathbb R^m\) by \[ \omega_r(f;\delta)_s: =\sup\{\|\Delta_h^rf(\cdot)\|_{L^s(\mathbb R^m)}; |h|\leq\delta\}, \] where \(r\in\mathbb N\), \(x,h,\delta\in\mathbb R^m\), \(\delta>0\), \
Anastassiou, George A., Gal, Sorin G.
openaire +3 more sources
Global smoothness preservation by singular integrals
Proyecciones (Antofagasta), 2018 Here is established that the well-known singular integrals of Picard, Poisson-Cauchy and Gauss- Weierstrass fulfill the "global smoothness preservation" property. J. e., they "ripple" less than the function they are applied on, that is producing a nice approximation to the unit. The associated inequalities are sharp.
G. Anastassiou
openaire +3 more sources
Global smoothness preservation with second order modulus of smoothness
Mathematica Slovaca, 2013 Abstract We establish the global smoothness preservation of a function f by the sequence of linear positive operators. Our estimate is in terms of the second order Ditzian-Totik modulus of smoothness. Application is given to the Bernstein operator.
G. Tachev
openaire +2 more sources
Global smoothness and approximation by generalized discrete singular operators
Journal of Numerical Analysis and Approximation Theory, 2014 In this article we continue with the study of generalized discrete singular operators over the real line regarding their simultaneous global smoothness preservation property with respect to \(L_{p}\) norm for \( 1\leq p\leq \infty ,\) by involving ...
George A. Anastassiou, Merve Kester
doaj +4 more sources
Best Constants in Global Smoothness Preservation Inequalities for Some Multivariate Operators
Journal of Approximation Theory, 1999 Using a probabilistic representation of positive operators going back to the classical paper of S. Bernstein the authors give sharp estimates for the modulus of continuity of \(L_tf\). Here \(\{L_t\xi_{t\in T}\) is an approximating family of positive operators acting in the space \(\{f:I^k\to\mathbb{R}\); \(\sup_{x,y}| f(x)-f(y)|
de la Cal, Jesús, Valle, Ana M.
openaire +3 more sources
Global smoothness preservation by bivariate interpolation operators
Analysis in Theory and Applications, 2003 The authors extend some interesting results proved earlier by themselves in the univariate case to the bivariate one. They also remark that the results can easily be extended for \(m\) \((> 2)\) variables, too. More precisely they prove that the bivariate interpolation polynomials of Hermite-Fejér based on the Chebyshev nodes of the first kind, those ...
Gal, S. G., Szabados, J.
openaire +3 more sources
Applied Mathematics Letters, 2011 The author continues with his study of multivariate smooth general singular integral operators over \(\mathbb R^N\), \(N\geq 1\), regarding their simultaneous global smoothness preservation property with respect to the \(L_p\) norm, \(1\leq p\leq \infty \), by involving multivariate higher order moduli of smoothness. Also, he studies their multivariate
G. Anastassiou
openaire +3 more sources
Best constants in preservation of global smoothness for Szász–Mirakyan operators
Journal of Mathematical Analysis and Applications, 2008 For \(t>0\), the Szász-Mirakyan operator \(S_{t}\) is defined by \[ S_{t}f(x):=e^{-xt}\,\sum_{k=0}^{\infty}f\Big(\frac{k}{t}\Big)\frac{(tx)^{k}}{k!}, \quad x\geq 0, \] where \(f\) is any real function defined on \([0,\,\infty)\) such that \(S_{t}| f| (x)0, \quad C_{t}:=\sup_{\delta>0}C_{t}(\delta), \] where \[ w(f;\delta):=\sup\big\{| f(x)-f(y)| \,:x,y\
Adell, José A., Lekuona, Alberto
openaire +3 more sources