<?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%">Bouraya, C</style></author><author><style face="normal" font="default" size="100%">Seddik, A</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">On the characterizations of some distinguished subclasses of Hilbert space operators</style></title><secondary-title><style face="normal" font="default" size="100%">Acta Scientiarum Mathematicarum</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2018</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer</style></publisher><volume><style face="normal" font="default" size="100%">84</style></volume><pages><style face="normal" font="default" size="100%">611-627</style></pages><isbn><style face="normal" font="default" size="100%">2064-8316</style></isbn><language><style face="normal" font="default" size="100%">eng</style></language><issue><style face="normal" font="default" size="100%">3</style></issue></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%">Chebbah, H</style></author><author><style face="normal" font="default" size="100%">Mennouni, A</style></author><author><style face="normal" font="default" size="100%">Ramdani, NE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Numerical Solution of Generalized Logarithmic Integral Equations of the Second Kind by Projections</style></title><secondary-title><style face="normal" font="default" size="100%">Malaysian Journal of Mathematical Sciences</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2018</style></year></dates><volume><style face="normal" font="default" size="100%">12</style></volume><pages><style face="normal" font="default" size="100%">349–367-349–367</style></pages><isbn><style face="normal" font="default" size="100%">2289-750X</style></isbn><language><style face="normal" font="default" size="100%">eng</style></language><issue><style face="normal" font="default" size="100%">3</style></issue></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%">Chaima Bouraya</style></author><author><style face="normal" font="default" size="100%">Seddik Ameur</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">On the characterizations of some distinguished subclasses of Hilbert space operators</style></title><secondary-title><style face="normal" font="default" size="100%">Acta Scientiarum Mathematicarum</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2018</style></year></dates><volume><style face="normal" font="default" size="100%">84</style></volume><pages><style face="normal" font="default" size="100%">611-627</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p style=&quot;text-align: justify;&quot;&gt;
	In this note, we present several characterizations for some distinguished classes of bounded Hilbert space operators (self-adjoint operators, normal operators, unitary operators, and isometry operators) in terms of operator inequalities.
&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">34</style></issue></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%">Abdelaziz Mennouni</style></author><author><style face="normal" font="default" size="100%">Nedjem-Eddine Ramdani</style></author><author><style face="normal" font="default" size="100%">Khaled Zennir</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A New Class of Fredholm Integral Equations of the Second Kind with Non Symmetric Kernel: Solving by Wavelets Method</style></title><secondary-title><style face="normal" font="default" size="100%">Boletim da Sociedade Paranaense de Matem´atica</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2018</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p style=&quot;text-align: justify;&quot;&gt;
	In this paper, we introduce an efficient modification of the wavelets method to solve a new class of Fredholm integral equations of the second kind with non symmetric kernel. This method based on orthonormal wavelet basis, as a consequence three systems are obtained, a Toeplitz system and two systems with condition number close to 1. Since the preconditioned conjugate gradient normal equation residual (CGNR) and preconditioned conjugate gradient normal equation error (CGNE) methods are applicable, we can solve the systems in O(2n log(n)) operations, by using the fast wavelet transform and the fast Fourier transform.
&lt;/p&gt;
</style></abstract></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%">Hasna CHEBBAH</style></author><author><style face="normal" font="default" size="100%">Abdelaziz Mennouni</style></author><author><style face="normal" font="default" size="100%">Nedjem-Eddine Ramdani</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Numerical Solution of Generalized Logarithmic Integral Equations of the Second Kind by Projections</style></title><secondary-title><style face="normal" font="default" size="100%">Malaysian Journal of Mathematical Sciences</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2018</style></year></dates><volume><style face="normal" font="default" size="100%">12</style></volume><pages><style face="normal" font="default" size="100%">349–367</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p style=&quot;text-align: justify;&quot;&gt;
	In this work, we present a new techniques to solve the integral equations of the second kind with logarithmic kernel. First, we show the existence and uniqueness of the solution for the given problem in a Hilbert space. Next, we discuss a projection method for solving integral equations with logarithmic kernel of the second kind; the present method based on the shifted Legendre polynomials. We examine the existence of the solution for the approximate equation, and we provide a new error estimate for the numerical solutions. At the end, numerical examples are provided to illustrate the theoretical results.
&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue></record></records></xml>