ICRAMI 2021 CONFERENCE - Bendjenna, Pr Hakim; Boumaza, Nouri; Meraoumia, Abdallah; Ouannas, Adel; Laimeche, Lakhdar; Abdelmalek, Salem

HERIMITIAN SOLUTIONS TO THE EQUATION AXA+ BY B= C, FOR HILBERT SPACE OPERATORS - Amina Boussaid; Farida Lombarkia (2021)

Maximization of the Stability Radius of an Infinite Dimensional System Subjected to Stochastic Unbounded Structured Multi-perturbations With Unbounded Input Operator - Amina, Heddar; Maissa, Kada (2021 International Conference on Recent Advances in Mathematics and Informatics (ICRAMI), 2021)

A new class of fredholm integral equations of the second kind with non symmetric kernel: solving by wavelets method - Abdelaziz Mennouni; Ramdani, Nedjem Eddine; Khaled Zennir (Boletim da Sociedade Paranaense de Matemática, 2021)

Operator equations and inner inverses of elementary operators - Lombarkia, F; Boussaid, A (Linear and Multilinear Algebra, 2021)

Robust Stabilization of Infinite Dimensional Systems Subjected to Stochastic and Deterministic Perturbations - Amira, Kameche; Maissa, Kada (2021 International Conference on Recent Advances in Mathematics and Informatics (ICRAMI), 2021)

Some representations of moore-penrose inverse for the sum of two operators and the extension of the fill-fishkind formula - Kara, Abdessalam; Said Guedjiba (Numerical Algebra, Control & Optimization, 2021)

Stability of the transmission plate equation with a delay term in the moment feedback control - Ghecham, Wassila; Rebiai, Salah‐Eddine; Sidiali, Fatima Zohra (Mathematical Methods in the Applied Sciences, 2021)

The stability radius of an infinite dimensional system subjected to stochastic unbounded structured multi-perturbations with application - Amina, Heddar; Maissa, Kada (International Conference on Research in Applied Mathematics and Computer Science, 2021)

Stabilization of coupled wave equations with boundary or internal distributed delay - Ghecham, Wassila; Salah-eddine Rebiai; Sidiali, Fatima Zohra (Applicable Analysis, 2021)

Stabilization of the wave equation with a nonlinear delay term in the boundary conditions - Ghecham, Wassila; Salah-eddine Rebiai; Sidiali, Fatima Zohra (Journal of Applied Analysis, 2021)

Generalized derivation, SVEP, finite ascent, range closure - Farida Lombarkia; Megri, Sabra (Filomat, 2020)

Improvement by projection for integro‐differential equations - Abdelaziz Mennouni (Mathematical Methods in the Applied Sciences, 2020)

Selfadjoint operators, normal operators, and characterizations - AMEUR SEDDIK (Operators and Matrices, 2019)

SOME PROPERTIES OF COMMON HERMITIAN SOLUTIONS OF MATRIX EQUATIONS A1XA - Warda Merahi; Said Guedjiba (2019)

SOME PROPERTIES OF COMMON HERMITIAN SOLUTIONS OF MATRIX EQUATIONS A1XA*1= B1 AND A2XA∗2 = B2 - Warda Merahi; Said Guedjiba (MATEMATICKI VESNIK ˇ MATEMATIQKI VESNIK, 2019)

On Numerical Radius Inequalities for Operator Matrices - Hanane Guelfen; Fuad Kittaneh (Numerical Functional Analysis and Optimization, 2019)

SELFADJOINT OPERATORS, NORMAL OPERATORS, AND CHARACTERIZATIONS - Seddik Ameur (Operators and Matrices, 2019)
Let B(H) be the C∗ -algebra of all bounded linear operators acting on a complex separable Hilbert space H . We shall show that: 1. The class of all selfadjoint operators in B(H) multiplied by scalars is characterized by ∀X ∈ B(H), S2X +XS2 =>2||SXS||, (S ∈ B(H)). 2. The class of all normal operators in B(H) is characterized by each of the three following properties (where DS = S∗S−SS∗ , for S ∈ B(H)), (i) ∀X ∈ B(H), S2X + XS2 =>2||SXS||,(S ∈ B(H)), (ii) S∗DSS = 0 = SDSS∗,(S ∈ B(H)), (iii) S∗DSS=> 0 =>SDSS∗,(S ∈ B(H)).

Operator equations and inner inverses of elementary operators - Farida Lombarkia; Amina Boussaid (Linear and Multilinear Algebra, 2019)
Let E,F,G,D be infinite complex Banach spaces and B(F,E) the Banach space of all bounded linear operators from F into E. Consider A1,A2∈B(F,E), B1,B2∈B(D,G)B1,B2∈B(D,G). Let MA1,B1:X→A1XB1 be the multiplication operator on B(G,F) induced by A1,B1. In particular, LA1=MA1,I and RB1=MI,B1, where I is the identity operator are the left and the right multiplication operators, respectively. The elementary operator Ψ defined on B(G,F)B(G,F) is the sum of two multiplication operators Ψ=MA1,B1+MA2,B2. This paper gives necessary and sufficient conditions for the existence of a common solution of the operator equations MA1,B1(X)=C1 and MA2,B2(X)=C2 and derive a new representation of the general common solution via the inner inverse of the elementary operator Ψ; we apply this result to determine new necessary and sufficient conditions for the existence of a Hermitian solution and a representation of the general Hermitian solution to the operator equation MA,B(X)=C. As a consequence, we obtain well-known results of Dajic´ and Koliha.

On the characterizations of some distinguished subclasses of Hilbert space operators - Bouraya, C; Seddik, A (Acta Scientiarum Mathematicarum, 2018)

Numerical Solution of Generalized Logarithmic Integral Equations of the Second Kind by Projections - Chebbah, H; Mennouni, A; Ramdani, NE (Malaysian Journal of Mathematical Sciences, 2018)

On the characterizations of some distinguished subclasses of Hilbert space operators - Chaima Bouraya; Seddik Ameur (Acta Scientiarum Mathematicarum, 2018)
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.

A New Class of Fredholm Integral Equations of the Second Kind with Non Symmetric Kernel: Solving by Wavelets Method - Abdelaziz Mennouni; Nedjem-Eddine Ramdani; Khaled Zennir (Boletim da Sociedade Paranaense de Matem´atica, 2018)
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.

Numerical Solution of Generalized Logarithmic Integral Equations of the Second Kind by Projections - Hasna CHEBBAH; Abdelaziz Mennouni; Nedjem-Eddine Ramdani (Malaysian Journal of Mathematical Sciences, 2018)
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.

Discrete septic spline quasi-interpolants for solving generalized Fredholm integral equation of the second kind via three degenerate kernel methods - Abdelaziz Mennouni; Saliha Zaouia (Mathematical Sciences, 2017)

Piecewise constant Galerkin method for a class of Cauchy singular integral equations of the second kind in L2 - Abdelaziz Mennouni (Journal of Computational and Applied Mathematics, 2017)

Uniform stabilization of the fourth order Schrödinger equation - Belkacem Aksas; Salah-eddine Rebiai (Journal of Mathematical Analysis and Applications, 2017)

Stabilization of the Fourth Order Schrödinger Equation - Belkacem Aksas; Salah-eddine Rebiai (New Trends in Analysis and Interdisciplinary Applications, 2017)
We study both boundary and internal stabilization problems for the fourth order Schrödinger equation in a smooth bounded domain Ω of Rn. We first consider the boundary stabilization problem. By introducing suitable dissipative boundary conditions, we prove that the solution decays exponentially in an appropriate energy space. In the internal stabilization problem, by assuming that the damping term is effective on the neighborhood of the boundary, we prove the exponential decay of the L2(Ω)-energy of the solution. Both results are established by using multipliers technique and compactness/uniqueness arguments.

Discrete septic spline quasi-interpolants for solving generalized Fredholm integral equation of the second kind via three degenerate kernel methods - Abdelaziz Mennouni; Saliha Zaouia (Mathematical Sciences, 2017)
Three main contributions are presented in this paper. First, the septic quasi-interpolants are calculated with all their coefficients. Second, we explore the results to solve a generalized and broad class of Fredholm integral equations of the second kind. Finally, we present three degenerate kernel methods; the latter is a combination of the two previously established methods in the literature. Moreover, we provide a convergence analysis and we give new error bounds. Finally, we exhibit some numerical examples and compare them with previous results in the literature.

Piecewise constant Galerkin method for a class of Cauchy singular integral equations of the second kind in L2 - Abdelaziz Mennouni (Journal of Computational and Applied Mathematics, 2017)
In this work, we present piecewise constant Galerkin method for a class of Cauchy singular integral equations of the second kind with constant coefficients in L2([0,1],C), using a sequence of orthogonal finite rank projections. We prove the existence and uniqueness theorems for the Cauchy integral equation and the approximate equation, respectively. We perform the error analysis for which we give new and improved estimates for the rates of convergence. Numerical example illustrates the theoretical results.

FINITE TIME BLOW-UP OF SOLUTIONS FOR A NONLINEAR SYSTEM OF FRACTIONAL DIFFERENTIAL EQUATIONS - Abdelaziz Mennouni; Abderrahmane Youkana (Electronic Journal of Differential Equations, 2017)

Asymmetric Fuglede Putnam's Theorem for operators reduced by their eigenspaces - Farida Lombarkia; Mohamed Amouch (FILOMAT, 2017)
Fuglede-Putnam Theorem have been proved for a considerably large number of class of operators. In this paper by using the spectral theory, we obtain a theoretical and general framework from which Fuglede-Putnam theorem may be promptly established for many classes of operators.

Asymmetric Fuglede Putnam's Theorem for operators reduced by their eigenspaces - Farida Lombarkia; Mohamed Amouch (arXiv preprint arXiv:1603.07494, 2016)

Uniform exponential stability of the transmission wave equation with a delay term in the boundary feedback - Salah-eddine Rebiai; Ali, FZ Sidi (IMA Journal of Mathematical Control and Information, 2016)

Uniform exponential stability of the transmission wave equation with a delay term in the boundary feedback - Salah-eddine Rebiai; Fatima Zohra Sidi-Ali (IMA Journal of Mathematical Control and Information, 2016)
We consider a system of transmission of the wave equation with Neumann feedback control that contains a delay term and acts on the exterior boundary. First, we prove under some assumptions that the closed-loop system generates a C 0 -semigroup of contractions on an appropriate Hilbert space. Then, under further assumptions, we show that the closed-loop system is exponentially stable. To establish this result, we introduce a suitable energy function and use multiplier method together with an estimate taken from Lasiecka & Triggiani (1992, Appl. Math. Optim., 25, 189–244.) (Lemma 7.2) and compactness-uniqueness argument.