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＜電子ブック＞
Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations / by Józef Banaś, Mohammad Mursaleen

版	1st ed. 2014.
出版者	(New Delhi : Springer India : Imprint: Springer)
出版年	2014
大きさ	XII, 315 p : online resource
著者標目	*Banaś, Józef author Mursaleen, Mohammad author SpringerLink (Online service)
件　名	LCSH:Functional analysis LCSH:Operator theory LCSH:Integral equations LCSH:Differential equations LCSH:Sequences (Mathematics) FREE:Functional Analysis FREE:Operator Theory FREE:Integral Equations FREE:Differential Equations FREE:Sequences, Series, Summability
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-81-322-1886-9

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