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This book delves into the topics of fixed-point theory as applied to block operator matrices within the context of Banach algebras featuring multi-valued inputs. Its scope extends to a broad range of equations, encompassing nonlinear biological models as well as two-dimensional boundary value problems associated with burgeoning cell populations and functional systems of differential and integral inclusions. The book systematically introduces the principles of topological fixed-point theory, offering insights into various classes of both single-valued and multi-valued maps. The overarching goal is to disseminate key techniques and outcomes derived from fixed-point theory, with a specific emphasis on its application to both single-valued and multi-valued mappings within the framework of Banach algebras.
Aref Jeribi is Professor in the Department of Mathematics, University of Sfax, Tunisia. He completed his habilitation of mathematics and applications at the University of Sfax, Tunisia, in 2002, and defended his Ph.D. thesis at the University of Corsica Pasquale Paoli, France, in 1998. His research interests include spectral theory, matrix operators, transport theory, Gribov operator, Bargmann space, fixed-point theory, Riesz basis and linear relations. He is author/co-author of 11 books and has published 229 research articles in reputed journals and conference proceedings.
Najib Kaddachi is Assistant Professor in the Department of Mathematics, Faculty of Economics and Management, University of Sfax, Tunisia. He completed his habilitation of mathematics and applications in 2021, and defended his Ph.D. thesis, in 2015, at the University of Sfax, Tunisia. His research interests lie in several areas of pure and applied mathematics, ordinary and partial differential equations, integral and differential inclusion, fixed-point theory, Banach algebra, functional analysis and operator theory.
Topological Structures.- Fixed-Point Theory in Suitable Banach Algebras.- Fixed-Point Theory for Block Operator Matrices.- Nonlinear One-Dimensional Boundary-Value Problems.- Two-Dimensional Boundary-Value Problems.- Existence Theory of Critical-Type of Fixed Point.- Two-Dimensional Value Problems for Differential Inclusion.
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