Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations (PDF)
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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.
M. MURSALEEN is professor of mathematics at Aligarh Muslim University, Aligarh. Earlier, he worked as professor of mathematics at King Abdulaziz University, Jeddah, Saudi Arabia, during 2004-2006. An active researcher, Prof. Mursaleen has authored two books and five book chapters, in addition to his contributions to 190 research papers to various international journals such as Proc. Amer. Math. Soc.,
- Autoren: Józef Banas , Mohammad Mursaleen
- 2014, 2014, 315 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 8132218868
- ISBN-13: 9788132218869
- Erscheinungsdatum: 18.07.2014
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- Größe: 2.98 MB
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“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)
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