@article {6573,
	title = {On the characterizations of some distinguished subclasses of Hilbert space operators},
	journal = {Acta Scientiarum Mathematicarum},
	volume = {84},
	number = {3},
	year = {2018},
	pages = {611-627},
	publisher = {Springer},
	isbn = {2064-8316},
	author = {Bouraya, C and Seddik, A}
}
@article {6570,
	title = {Numerical Solution of Generalized Logarithmic Integral Equations of the Second Kind by Projections},
	journal = {Malaysian Journal of Mathematical Sciences},
	volume = {12},
	number = {3},
	year = {2018},
	pages = {349{\textendash}367-349{\textendash}367},
	isbn = {2289-750X},
	author = {Chebbah, H and Mennouni, A and Ramdani, NE}
}
@article {5265,
	title = {On the characterizations of some distinguished subclasses of Hilbert space operators},
	journal = {Acta Scientiarum Mathematicarum},
	volume = {84},
	number = {34},
	year = {2018},
	pages = {611-627},
	abstract = {
	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.

},
	author = {Chaima Bouraya and Seddik Ameur}
}
@article {5261,
	title = {A New Class of Fredholm Integral Equations of the Second Kind with Non Symmetric Kernel: Solving by Wavelets Method},
	journal = {Boletim da Sociedade Paranaense de Matem{\textasciiacute}atica},
	year = {2018},
	abstract = {
	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.

},
	author = {Abdelaziz Mennouni and Nedjem-Eddine Ramdani and Khaled Zennir}
}
@article {5260,
	title = {Numerical Solution of Generalized Logarithmic Integral Equations of the Second Kind by Projections},
	journal = {Malaysian Journal of Mathematical Sciences},
	volume = {12},
	number = {3},
	year = {2018},
	pages = {349{\textendash}367},
	abstract = {
	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.

},
	author = {Hasna CHEBBAH and Abdelaziz Mennouni and Nedjem-Eddine Ramdani}
}
