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.
General
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