scholarly journals Asymptotic properties of Urysohn type generalized sampling operators

2021 ◽  
Vol 13 (3) ◽  
pp. 631-641
Author(s):  
H. Karsli
Keyword(s):  
Asymptotic Properties ◽  
Convergence Properties ◽  
Generalized Sampling ◽  
Linear And Nonlinear

The concern of this study is to continue the investigation of convergence properties of Urysohn type generalized sampling operators, which are defined by the author in [Dolomites Res. Notes Approx. 2021, 14 (2), 58-67]. In details, the paper centers around to investigation of the asymptotic properties together with some Voronovskaya-type theorems for the linear and nonlinear counterpart of Urysohn type generalized sampling operators.

scholarly journals On multidimensional Urysohn type generalized sampling operators

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Harun Karsli
Keyword(s):  
Asymptotic Properties ◽  
Dimensional Case ◽  
One Dimensional ◽  
Generalized Sampling

<p style='text-indent:20px;'>The concern of this study is to construction of a multidimensional version of Urysohn type generalized sampling operators, whose one dimensional case defined and investigated by the author in [<xref ref-type="bibr" rid="b28">28</xref>] and [<xref ref-type="bibr" rid="b27">27</xref>]. In details, as a continuation of the studies of the author, the paper centers around to investigation of some approximation and asymptotic properties of the aforementioned linear multidimensional Urysohn type generalized sampling operators.</p>

Applications of the Birkhoff–Hopf theorem to the spectral theory of positive linear operators

1995 ◽  
Vol 117 (3) ◽  
pp. 491-512 ◽  
Author(s):  
Simon P. Eveson ◽  
Roger D. Nussbaum
Keyword(s):  
Linear Operators ◽  
Vector Spaces ◽  
Ergodic Theorems ◽  
Convergence Properties ◽  
Nonlinear Integral Equations ◽  
Ordered Vector Spaces ◽  
Partially Ordered Vector Spaces ◽  
Linear And Nonlinear ◽  
Nonlinear Maps ◽  
Hopf Theorem

This paper may be regarded as a sequel to our earlier paper [19], where we give an elementary and self-contained proof of a very general form of the Hopf theorem on order-preserving linear operators in partially ordered vector spaces (reproduced here as Theorem 1·1).Versions of this theorem and related ideas have been used by various authors to study both linear and nonlinear integral equations (Thompson [41], Bushell [9, 11], Potter [38, 39], Eveson [16, 17], Bushell and Okrasiriski [12, 13]); the convergence properties of nonlinear maps (Nussbaum [32, 33]); so-called DAD theorems (Borwein, Lewis and Nussbaum [8]) and in the proof of weak ergodic theorems (Fujimoto and Krause [20], Nussbaum [34]).

scholarly journals Estimation of Partial derivatives of the average of densities belonging to a family of densities

1975 ◽  
Vol 20 (2) ◽  
pp. 230-241 ◽  
Author(s):  
V. Susarla ◽  
S. Kumar
Keyword(s):  
Lebesgue Measure ◽  
Empirical Bayes ◽  
Mean Squared Error ◽  
Asymptotic Properties ◽  
Convergence Properties ◽  
Kernel Estimates ◽  
Partial Derivatives ◽  
Squared Error ◽  
The Mean ◽  
Derivatives Of

Recently, attention has been drawn to the problem of estimation of a k-variate probability density and its partial derivatives of various orders. Specifically, let X1, …, Xn be i.i.d. k-variate random variables with common density f wrt Lebesgue measure μ on the k-dimensional σ-field Bk. Parzen (1962) in the k = 1 case and Cacoullos (1966) in the k ≧ 1 case gave the asymptotic properties of a class of kernel estimates fn(x), x ∈ Rk, of f(x) based on X1, …, Xn. The asymptotic properties given in the above two papers concern consistency, asymp-totic unbiasedness, bounds for the mean squared error and asymptotic normality of fn. Also in the context of an empirical Bayes two-action problem, Johns and Van Ryzin (1972) introduced kernel estimates for f(x) and the derivative f'(x)for x∈R1 when f is a mixture of univariate exponential densities wrt Lebesgue measure on B1. They also investigated the asymptotic unbiasedness and themean squared error convergence properties of these estimates. Lin (1968) statedsome generalizations of the results of Johns and Van Ryzin, with applicationsto empirical Bayes decision problems.

Convergence properties of hit-and-run samplers

1998 ◽  
Vol 14 (4) ◽  
pp. 767-800
Author(s):  
Claude Bélisle ◽  
Arnon Boneh ◽  
Richard J. Caron
Keyword(s):  
Convergence Properties ◽  
Hit And Run

Linear and Nonlinear Optical Properties of Natural Dyes Freestanding Films and Application in Optical Limiting

2020 ◽  
pp. 139-143
Keyword(s):  
Absorption Coefficient ◽  
Water Solution ◽  
Optical Limiting ◽  
Refraction Index ◽  
Laser Wavelength ◽  
Solid State Laser ◽  
Natural Dyes ◽  
Linear And Nonlinear ◽  
532 Nm ◽  
Absorbance Spectra

Natural dyes were followed and prepared from a pomegranate, purple carrot, and eggplant peel. The absorbance spectra was measured in the wavelength range 300-800 nm. The linear properties measurements of the prepared natural dye freestanding films were determined include absorption coefficient (α0), extinction coefficient (κ), and linear refraction index (n). The nonlinear refractive index n2 and nonlinear absorption coefficient β2 of the natural dyes in the water solution were measured by the optical z-scan technique under a pumped solid state laser at a laser wavelength of 532 nm. The results indicated that the pomegranate dye can be promising candidates for optical limiting applications with significantly low optical limiting of 3.5 mW.

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