Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations by Józef BanaSequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations by Józef Bana

Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral…

byJózef Bana, Mohammad Mursaleen

Hardcover | August 1, 2014

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This book deals with the study of sequence spaces, matrix transformations, measures of noncompactness and their various applications. The notion of measure of noncompactness is one of the most useful ones available and has many applications. The book discusses some of the existence results for various types of differential and integral equations with the help of measures of noncompactness; in particular, the Hausdorff measure of noncompactness has been applied to obtain necessary and sufficient conditions for matrix operators between BK spaces to be compact operators.

The book consists of eight self-contained chapters. Chapter 1 discusses the theory of FK spaces and Chapter 2 various duals of sequence spaces, which are used to characterize the matrix classes between these sequence spaces (FK and BK spaces) in Chapters 3 and 4. Chapter 5 studies the notion of a measure of noncompactness and its properties. The techniques associated with measures of noncompactness are applied to characterize the compact matrix operators in Chapters 6. In Chapters 7 and 8, some of the existence results are discussed for various types of differential and integral equations, which are obtained with the help of argumentations based on compactness conditions.

JÓZEF BANAÅ is professor of mathematics and chair at the Department of Mathematics in Rzeszow University of Technology, Poland. He is on the editorial committee of many journals of international repute:Commentationes Mathematicae(Polish Mathematical Society),Abstract and Applied Analysis(Hindawi Corporation),Journal of Inequalities and...
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Title:Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral…Format:HardcoverDimensions:315 pagesPublished:August 1, 2014Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:813221885X

ISBN - 13:9788132218852

Reviews

Table of Contents

Chapter 1. Introduction to FK spaces.-Chapter 2. Matrix Transformations.-Chapter 3. Some new sequence spaces of non-absolute type.-Chapter 4. Some non-classical sequence spaces.-Chapter 5. Measures of noncompactness.-Chapter 6. Application to compact matrix operators.-Chapter 7. Applications to infinite systems of differential equations.-Chapter 8. Applications to integral equations.

Editorial Reviews

"This book deals with some aspects of the theory of sequence spaces and operators acting between them. . The book consists of eight chapters. Each chapter contains exercises and references. . the book will be useful for all specialists in functional analysis since it contains a lot of new and interesting results." (P. P. Zabreiko, Mathematical Reviews, August, 2015)"This is one of few books out there in which varioustypes of measures of noncompactness are covered so extensively with theinclusion of the applications to compact matrix operators, infinite systems ofdifferential equations and integral equations. . The presentation is clear andself-contained throughout the entire treatment. Proofs of the main results aredetailed and elegant. The book is suitable for graduate students andresearchers with interest in generalized compactness methods for solving differentialand integral equations." (Dhruba Adhikari, zbMATH 1323.47001, 2015)