Nonlinear Functional Analysis in Banach Spaces and Banach Algebras: Fixed Point Theory under Weak Topology for Nonlinear Operators and Block Operator Matrices with Applications, 1st Edition (Hardback) book cover

Nonlinear Functional Analysis in Banach Spaces and Banach Algebras

Fixed Point Theory under Weak Topology for Nonlinear Operators and Block Operator Matrices with Applications, 1st Edition

By Aref Jeribi, Bilel Krichen

Chapman and Hall/CRC

371 pages

Purchasing Options:$ = USD
Hardback: 9781498733885
pub: 2015-08-14
SAVE ~$26.00
$130.00
$104.00
x
eBook (VitalSource) : 9780429069826
pub: 2015-08-14
from $28.98


FREE Standard Shipping!

Description

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.

Table of Contents

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

About the Authors

Author

Aref Jeribi

Sfax, Department of Mathematics, Tunisia

Learn more about Aref Jeribi >>

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.

About the Series

Chapman & Hall/CRC Monographs and Research Notes in Mathematics

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT004000
MATHEMATICS / Arithmetic
MAT007000
MATHEMATICS / Differential Equations
MAT037000
MATHEMATICS / Functional Analysis