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

This book deals with the study of sequence spaces, matrix transformations, measures of non compactness and their various applications. The notion of measure of non compactness is one of the most useful notions, which has many applications.§The book discusses some existence results for various types of functional, differential and integral equations with the help of measures of non compactness; in particular, the Hausdorff measure of non compactness has been extensively used in the characterization of compact operators between infinite-dimensional Banach spaces. The Hausdorff measure of non compactness has been applied to obtain necessary and sufficient conditions for matrix operators between BK spaces to be compact operators.§The book consists of nine chapters. Every chapter is written in a self-contained style. 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 measures of non compactness and their properties and applies these techniques to characterize the compact matrix operators in Chapters 6. In Chapters 7 and 8, some existence results are discussed for various types of differential and integral equations, which are obtained with the help of argumentations based on compactness conditions.§