<?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%">IOANNIS K. ARGYROS</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON THE SOLUTION OF EQUATIONS AND APPLICATIONS ON BANACH SPACE VALUED FUNCTIONS AND FRACTIONAL VECTOR CALCULI</style></title><secondary-title><style face="normal" font="default" size="100%">On the Solution of Equations  </style></secondary-title><alt-title><style face="normal" font="default" size="100%">CAA</style></alt-title><short-title><style face="normal" font="default" size="100%">On the Solution of Equations</style></short-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A33</style></keyword><keyword><style  face="normal" font="default" size="100%">46B25</style></keyword><keyword><style  face="normal" font="default" size="100%">47J05</style></keyword><keyword><style  face="normal" font="default" size="100%">47J25</style></keyword><keyword><style  face="normal" font="default" size="100%">65G99</style></keyword><keyword><style  face="normal" font="default" size="100%">65H10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">06/2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/21/3/5.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">21</style></volume><pages><style face="normal" font="default" size="100%">20</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;The aim of this paper is to solve equations on Banach space&amp;nbsp;using iterative methods under generalized conditions. The differentiability of&amp;nbsp;the operator involved is not assumed and its domain is not necessarily convex.&amp;nbsp;Several applications are suggested &amp;nbsp;including Banach space valued functions of&amp;nbsp;abstract fractional calculus, where all integrals are of Bochner-type.&lt;br /&gt;
&amp;nbsp;&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%">405</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><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%">SHELL MIXED FRACTIONAL OSTROWSKI 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%">SHELL MIXED FRACTIONAL OSTROWSKI INEQUALITIES</style></short-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A33</style></keyword><keyword><style  face="normal" font="default" size="100%">26D10</style></keyword><keyword><style  face="normal" font="default" size="100%">26D15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/15/1/8.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">15</style></volume><pages><style face="normal" font="default" size="100%">112</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;Very general shell mixed Caputo fractional Ostrowski inequalities are presented, radial and non-radial cases. One of them is proved to be sharp and attained. Estimates are with respect to ||·||&lt;sub&gt;p&lt;/sub&gt; , 1 ≤ p ≤ ∞.&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%">101</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><author><style face="normal" font="default" size="100%">SORIN G. GAL</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">QUANTITATIVE ESTIMATES IN THE OVERCONVERGENCE OF SOME SINGULAR INTEGRALS</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%">OVERCONVERGENCE OF SOME SINGULAR INTEGRALS</style></short-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">32E30</style></keyword><keyword><style  face="normal" font="default" size="100%">41A25.</style></keyword><keyword><style  face="normal" font="default" size="100%">41A35</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%">01/2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/14/1/2.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%">20</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 paper we obtain quantitative estimates in the overconvergence phenomenon for the classical singular integrals of Gauss-Weierstrass, Poisson-Cauchy and Picard.&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%">13</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%">RIEMANN-LIOUVILLE FRACTIONAL OPIAL INEQUALITIES FOR SEVERAL FUNCTIONS WITH APPLICATIONS</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A33</style></keyword><keyword><style  face="normal" font="default" size="100%">26D10</style></keyword><keyword><style  face="normal" font="default" size="100%">26D15</style></keyword><keyword><style  face="normal" font="default" size="100%">34A12</style></keyword><keyword><style  face="normal" font="default" size="100%">34A99</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/12/4/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">12</style></volume><pages><style face="normal" font="default" size="100%">22</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;A large variety of very general ${ L_p(1 ≤ p ≤ ∞) }$ form Opial type inequalities ([15]) is presented involving Riemann-Liouville fractional derivatives ([5], [12], [13], [14]) of several functions in different orders and powers. From the established results derive several other particular results of special interest. Applications of some of these special inequalities are given in proving uniqueness of solution and in giving upper bounds to solutions of initial value fractional problems involving a very general system of several fractional differential equations. Upper bounds to various Riemann-Liouville fractional derivatives of the solutions that are involved in the above systems are given too.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">377</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 MULTIVARIATE OPIAL TYPE INEQUALITIES OVER SPHERICAL SHELLS</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 Multivariate Opial Type Inequalities</style></short-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A33</style></keyword><keyword><style  face="normal" font="default" size="100%">26D10</style></keyword><keyword><style  face="normal" font="default" size="100%">26D15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">04/2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/11/2/5.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">11</style></volume><pages><style face="normal" font="default" size="100%">233</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;div&gt;Here is introduced the concept of multivariate fractional differentiation especially of the fractional radial differentiation, by extending the univariate definition of Canavati [11]. Then we produce Opial type nequalities over compact and convex subsets of R&lt;sup&gt;N&lt;/sup&gt;, N ≥ 2, mainly over spherical shells, studying the problem in all possibilities. Our results involve one, or two, or more functions.&lt;/div&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><work-type><style face="normal" font="default" size="100%">scientific: mathematics</style></work-type><section><style face="normal" font="default" size="100%">201</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%">MULTIVARIATE FRACTIONAL TAYLOR’S FORMULA</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%">Multivariate Fractional Taylor’s Formula</style></short-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A33</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">04/2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/11/2/4.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">11</style></volume><pages><style face="normal" font="default" size="100%">199</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;Here is established a multivariate fractional Taylor’s formula using a suitable definition of fractional derivative. As related results we present that the order of fractional-ordinary partial differentiation is immaterial, we discuss fractional integration by parts, and we estimate the remainder of our multivariate fractional Taylor’s formula.&lt;/div&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><work-type><style face="normal" font="default" size="100%">scientific: mathematics</style></work-type><section><style face="normal" font="default" size="100%">189</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><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></records></xml>