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

by Jozef Banáš, Mohammad Mursaleen

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.

327 pages, Hardcover

First published May 20, 2014

About the author

Ever since Jozef Banas turned to writing full time in 2006, the popularity of his books has been on a constant rise. His creative home is Slovakia, a country with a population of five million seated right in the middle of Europe. Every year Banas publishes a new literary piece. His works include the #1 bestselling novels Code 9 and its sequel Code 1 about the life of Jesus in India which has become the subject of heated debate among readers. His documentary novel The Jubilation Zone is the most translated Slovak literary work. With more than 270,000 sold copies, statistically every eighth household in Slovakia owns one of Banas’ books. The community of his readers is growing fast at home as well as abroad. His books have been published in ten languages including Russian, German, Hindi and Arabic.
Jozef Banas is one of Slovakia’s most successful authors of the last decade. He is the holder of many literary awards, both domestic and international.
He has published four TV scenarios, one movie script, three theatre comedies, thirteen books in Slovakia, ten abroad.