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This is the first book to tackle the topological fixed point theory for block operator matrices with nonlinear entries in Banach spaces and algebras. The authors present several extensions of Schauder's and Krasnosel'skii's fixed point theorems to the class of weakly compact operators acting on Banach spaces and algebras. They also address under which conditions a 2×2 block operator matrix with single- and multi-valued nonlinear entries will have a fixed point. In addition, the book describes applications of fixed point theory to diverse equations.
List of contents
Fixed Point Theory: Fundamentals. Fixed Point Theory under Weak Topology. Fixed Point Theory in Banach Algebras. Fixed Point Theory for BOM on Banach Spaces and Banach Algebras. Applications in Mathematical Physics and Biology: Existence of Solutions for Transport Equations. Exsistence of Solutions for Nonlinear Integral Equations. Two-Dimensional Boundary Value Problems.
About the author
Aref Jeribi is a professor in mathematics at the University of Sfax.
Bilel Krichen is an associate professor in applied mathematics at the University of Sfax.
Summary
Uncover the Useful Interactions of Fixed Point Theory with Topological Structures
Nonlinear Functional Analysis in Banach Spaces and Banach Algebras: Fixed Point Theory under Weak Topology for Nonlinear Operators and Block Operator Matrices with Applications is the first book to tackle the topological fixed point theory for block operator matrices with nonlinear entries in Banach spaces and Banach algebras. The book provides researchers and graduate students with a unified survey of the fundamental principles of fixed point theory in Banach spaces and algebras.
The authors present several extensions of Schauder’s and Krasnosel’skii’s fixed point theorems to the class of weakly compact operators acting on Banach spaces and algebras, particularly on spaces satisfying the Dunford–Pettis property. They also address under which conditions a 2×2 block operator matrix with single- and multi-valued nonlinear entries will have a fixed point.
In addition, the book describes applications of fixed point theory to a wide range of diverse equations, including transport equations arising in the kinetic theory of gas, stationary nonlinear biological models, two-dimensional boundary-value problems arising in growing cell populations, and functional systems of integral equations. The book focuses on fixed point results under the weak topology since these problems involve the loss of compactness of mappings and/or the missing geometric and topological structure of their underlying domain.
