<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">George A. Anastassiou</style></author><author><style face="normal" font="default" size="100%">MERVE KESTER</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Lp APPROXIMATION WITH RATES BY GENERALIZED DISCRETE SINGULAR OPERATORS</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26D15</style></keyword><keyword><style  face="normal" font="default" size="100%">41A17</style></keyword><keyword><style  face="normal" font="default" size="100%">41A25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/19/2/5.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Here we give the approximation properties with rates of generalized discrete versions of Picard, Gauss-Weierstrass, and Poisson-Cauchy singular operators. We treat both the unitary and non-unitary cases of the operators above. We derive quantitatively ${Lp}$ convergence of these operators to the unit operator by involving the ${Lp}$ higher modulus of smoothness of an ${ Lp(\mathbb{R}) }$ function.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">217</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">George A. Anastassiou</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">FRACTIONAL TRIGONOMETRIC KOROVKIN THEORY</style></title><secondary-title><style face="normal" font="default" size="100%">Communications in Applied Analysis</style></secondary-title><short-title><style face="normal" font="default" size="100%">FRACTIONAL TRIGONOMETRIC KOROVKIN THEORY</style></short-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A33</style></keyword><keyword><style  face="normal" font="default" size="100%">41A17</style></keyword><keyword><style  face="normal" font="default" size="100%">41A25</style></keyword><keyword><style  face="normal" font="default" size="100%">41A36</style></keyword><keyword><style  face="normal" font="default" size="100%">41A80.</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2006</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/14/1/4.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">14</style></volume><pages><style face="normal" font="default" size="100%">58</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;div class=&quot;rtejustify&quot;&gt;In this article we study quantitatively with rates the trigonometric weak convergence of a sequence of finite positive measures to the unit measure. Equivalently we study quantitatively the trigonometric pointwise convergence of sequence of positive linear operators to the unit operator, all acting on continuous functions on [−π, π]. From there we derive with rates the corresponding trigonometric uniform convergence of the last. Our inequalities for all of the above in their right hand sides contain the moduli of continuity of the right and left Caputo fractional derivatives of the involved function. From our uniform trigonometric Shisha-Mond type inequality we derive the first trigonometric fractional Korovkin type theorem regarding the trigonometric uniform convergence of positive linear operators to the unit. We give applications, especially to Bernstein polynomials over [−π, π] for which we establish fractional trigonometric quantitative results.&lt;/div&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><work-type><style face="normal" font="default" size="100%">scientific: mathematics</style></work-type><section><style face="normal" font="default" size="100%">39</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">George A. Anastassiou</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">HIGHER ORDER FUZZY KOROVKIN THEORY VIA INEQUALITIES</style></title><secondary-title><style face="normal" font="default" size="100%">Communications in Applied Analysis</style></secondary-title><short-title><style face="normal" font="default" size="100%">Fuzzy Korovkin Theory</style></short-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26E50</style></keyword><keyword><style  face="normal" font="default" size="100%">28E10</style></keyword><keyword><style  face="normal" font="default" size="100%">41A17</style></keyword><keyword><style  face="normal" font="default" size="100%">41A25</style></keyword><keyword><style  face="normal" font="default" size="100%">41A36</style></keyword><keyword><style  face="normal" font="default" size="100%">47S40</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2006</style></year><pub-dates><date><style  face="normal" font="default" size="100%">12/2006</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/10/4/4.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">10</style></volume><pages><style face="normal" font="default" size="100%">503</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;Here is studied with rates the fuzzy uniform and L p , p ≥ 1, convergence of a sequence of fuzzy positive linear operators to the fuzzy unit operator acting on spaces of fuzzy differentiable functions. This is done quantitatively via fuzzy Korovkin type inequalities involving the fuzzy modulus of continuity of a fuzzy derivative of the engaged function. From there we deduce general fuzzy Korovkin type theorems with high rate of convergence. The surprising fact is that basic real positive linear operator simple assumptions enforce here the fuzzy convergences. At the end we give applications. Our results are univariate and multivariate. The assumptions are minimal and natural fulfilled by almost all example – fuzzy positive linear&lt;br /&gt;
operators.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><work-type><style face="normal" font="default" size="100%">scientific: mathematics</style></work-type><section><style face="normal" font="default" size="100%">469</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">George A. Anastassiou</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">HIGHER ORDER FUZZY KOROVKIN THEORY VIA INEQUALITIES</style></title><secondary-title><style face="normal" font="default" size="100%">Communications in Applied Analysis</style></secondary-title><short-title><style face="normal" font="default" size="100%">Higher Order Fuzzy Theory</style></short-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26E50</style></keyword><keyword><style  face="normal" font="default" size="100%">28E10</style></keyword><keyword><style  face="normal" font="default" size="100%">41A17</style></keyword><keyword><style  face="normal" font="default" size="100%">41A25</style></keyword><keyword><style  face="normal" font="default" size="100%">41A36</style></keyword><keyword><style  face="normal" font="default" size="100%">47S40</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2006</style></year><pub-dates><date><style  face="normal" font="default" size="100%">08/2006</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/10/3/7.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">10</style></volume><pages><style face="normal" font="default" size="100%">395</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;Here is studied with rates the fuzzy uniform and L p , p ≥ 1, convergence of a sequence of fuzzy positive linear operators to the fuzzy unit operator acting on spaces of fuzzy differentiable functions. This is done quantitatively via fuzzy Korovkin type inequalities involving the fuzzy modulus of continuity of a fuzzy derivative of the engaged function. From there we deduce general fuzzy Korovkin type theorems with high rate of convergence. The surprising fact is that basic real positive linear operator simple assumptions enforce here the fuzzy convergences. At the end we give applications. Our results are univariate and multivariate. The assumptions are minimal and natural fulfilled by almost all example—fuzzy positive linear operators.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><work-type><style face="normal" font="default" size="100%">scientific: mathematics</style></work-type><section><style face="normal" font="default" size="100%">361</style></section></record></records></xml>