M. MEZRAG Lahcene

Prof

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Department

Mathematics Department

Research Interests

Specialized in Mathematics Department. Focused on academic and scientific development.

Contact Info

University of M'Sila, Algeria

Email : lahcene.mezrag@univ-msila.dz

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Recent Publications

2024-05-01

Relationship between Sublinear Operators and their Subdifferentials for Certain Classes of Lipschitz Summability

Let SB(X, Y ) be the set of all bounded sublinear operators from a Banach space X into a complete Banach lattice Y ;
which is a pointed convex cone not salient in Lip0(X, Y ). In this paper, we are interested in studying the relationship between T and its
subdifferential ∇T (the set of all bounded linear operators u : X −→ Y such that u(x) ≤ T(x) for all x in X); concerning certain
notions of Lipschitz summability. We also answer negatively a question posed previously concerning this type of relation in the linear
case. For this, we introduce and study a new concept of summability in the category of Lipschitz operators, which we call ”super
Lipschitz p-summing operators”. We prove some characterizations in terms of a domination theorem and some properties of this notion.
Keywords: Banach lattice, Lipschitz p-dominated operator, Lipschitz p-summing operator, p-summing operator, sublinear operator
Citation

M. MEZRAG Lahcene, (2024-05-01), "Relationship between Sublinear Operators and their Subdifferentials for Certain Classes of Lipschitz Summability", [national] INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND SIMULATION, VOL. 01, NO. 01, MAY 2024 , Université de Biscra

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2023

Aperçu sur la géométrie des espaces de Banach

C'est l'étude des propriétés des espaces de Banach pour les classifier en examinant les propriétés géométriques de la boule unité ou les ensembles convexes. La compréhension de la GEB a été et continue d'être utile dans de nombreux domaine de mathématiques. Et l'utilisation de la logique, la théorie des ensembles et des groupes, l'analyse combinatoie nous donne des informations très riches sur la structure géométrique des espaces.
Citation

M. MEZRAG Lahcene, (2023), "Aperçu sur la géométrie des espaces de Banach", [national] First national applied mathematics seminar 1st-NAM'23 , Université de Biskra

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2022

Dominated multilinear operators defined on tensor products of Banach spaces

In this paper, we introduce and study new classes of dominated multilinear operators, which we call (p;p1,…,pn;G1,…,Gn)
-dominated and (p~;p1,…,pn;G1,…,Gn)
-dominated multilinear operators defined on the tensor product of Banach spaces. Some characterizations of this type of operators are given and we prove some important coincidence results. As an application, we characterize (p;p1,…,pn)
-dominated multilinear operators on C(K,G)
and (p;p1,…,pn)
-dominated multilinear operators in the sense of Dinculeanu on C(K,G)
, where K is a compact Hausdorff space and G a Banach space. We also treat the connection between an operator T and its associated operators Tt,T~
and T#
for certain classes.
Citation

M. MEZRAG Lahcene, (2022), "Dominated multilinear operators defined on tensor products of Banach spaces", [national] Advances in Operator Theory , Springer

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2021

Lipschitz p-lattice summing operators

In this paper, we introduce and study the notion of Lipschitz p-lattice summing operators in the category of Lipschitz operators which generalizes the class of p-lattice summing operators in the linear case. Some interesting properties are given. Also, some connections with other classes of operators are presented.
Citation

M. MEZRAG Lahcene, (2021), "Lipschitz p-lattice summing operators", [national] advances operators theory , spriger

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2018

Newclasses of summability for Lipschitz operators

Notre équipe a été formée selon la circulaire n 2 du 20 février 2018 qui concerne les modalités d’acceptation et de gestion des projets de recherche formation universitaire. Nous allons travailler sur la notion récente (2009) des opérateurs lipschitziens sommant. C’est le passage de la géomètrie des espaces de Banach (cas linéaire) au cas non linéaires. Plusieurs travaux on été réalisés dans ce domaine un peu partout. Nous avons contribué à l’avancement dans cette direction. On a collaboré avec plusieurs collègues de plusieurs universités étrangères et on a fait soutenir 3 doctorants. Deux autres doctorants sont en finalisation de thèse et qui ne figurent pas comme membre du projet. Nous voulons continuer avec de nouveaux doctorants qui sont membres de ce projet dans ce thème qui est encore relativement vierge.
Citation

M. MEZRAG Lahcene, (2018), "Newclasses of summability for Lipschitz operators", [international] International conference "New developments in complex analysis and function theory" , University of Crete, Greece

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