Nonlinear Functional Analysis in Banach Spaces and Banach Algebras : Fixed Point Theory Under Weak Topology for Nonlinear Operators and Block Operator Matrices With Applications

Jeribi, Aref; Krichen, Bilel

ISBN 10: 1498733883 / ISBN 13: 9781498733885

Published by Chapman and Hall/CRC, 2015

About this Item

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Bibliographic Details

• Title: Nonlinear Functional Analysis in Banach Spaces and Banach Algebras : Fixed Point Theory Under Weak Topology for Nonlinear Operators and Block Operator Matrices With Applications
• Publisher: Chapman and Hall/CRC
• Publication Date: 2015
• Language: English
• ISBN 10: 1498733883
• ISBN 13: 9781498733885
• Binding: Hardcover
• Condition: As New

About this title

Synopsis

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.

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.