1st Edition
Nonlinear Functional Analysis in Banach Spaces and Banach Algebras Fixed Point Theory under Weak Topology for Nonlinear Operators and Block Operator Matrices with Applications
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.
Fixed Point Theory
Fundamentals
Basic Tools in Banach Spaces
Contraction Mappings
Weak Topology
Measure of Weak Noncompactness (MNWC)
Basic Tools in Banach Algebras
Elementary Fixed Point Theorems
Positivity and Cones
Fixed Point Theory under Weak Topology
Fixed Point Theorems in DP Spaces and Weak Compactness
Banach Spaces and Weak Compactness
Fixed Point Theorems and MNWC
Fixed Point Theorems for Multi-valued Mappings
Some Leray–Schauder’s Alternatives
Fixed Point Theory in Banach Algebras
Fixed Point Theorems Involving Three Operators
WC–Banach Algebras
Leray–Schauder’s Alternatives in Banach Algebras Involving Three Operators
Convex-Power Condensing Operators
ws-Compact and ω-Convex-Power Condensing Maps
Fixed Point Theory for BOM on Banach Spaces and Banach Algebras
Some Variants of Schauder’s and Krasnosel’skii’s Fixed Point Theorems for BOM
Fixed Point Theory under Weak Topology Features
Fixed Point Theorems for BOM in Banach Algebras
Fixed Point Results in a Regular Case
BOM with Multi-Valued Inputs
Applications in Mathematical Physics and Biology
Existence of Solutions for Transport Equations
Transport Equations in the Kinetic Theory of Gas
Transport Equations Arising in Growing Cell Population
Existence of Solutions for Nonlinear Integral Equations
Existence of Solutions for Hammerstein’s Integral Equation
A Study of Some FIEs in Banach Algebras
Existence Results for FDEs in Banach Algebras
An Application of Leray–Schauder’s Theorem to FIEs
Two-Dimensional Boundary Value Problems
A System of Transport Equations in Lp (1 < p < ∞)
A Study of a Biological Coupled System in L1
A Coupled Functional Integral System in Banach Algebras
A Coupled System in Banach Algebras under the Condition (P)
Nonlinear Equations with Unbounded Domain
Differential Inclusions
Biography
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.
