Table of contents

  1. Front Matter
    Pages i-xii
  2. Józef Banaś, Mohammad Mursaleen
    Pages 1-32
  3. Józef Banaś, Mohammad Mursaleen
    Pages 33-70
  4. Józef Banaś, Mohammad Mursaleen
    Pages 71-103
  5. Józef Banaś, Mohammad Mursaleen
    Pages 105-146
  6. Józef Banaś, Mohammad Mursaleen
    Pages 147-184
  7. Józef Banaś, Mohammad Mursaleen
    Pages 185-218
  8. Józef Banaś, Mohammad Mursaleen
    Pages 219-262
  9. Józef Banaś, Mohammad Mursaleen
    Pages 263-310
  10. Back Matter
    Pages 311-315

About this book

Introduction

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.

Keywords

Compact operators Differential and integral equations Matrix transformations Measures of noncompactness Sequence spaces

Authors and affiliations

  • Józef Banaś
    • 1
  • Mohammad Mursaleen
    • 2
  1. 1.Department of MathematicsRzeszów University of TechnologyRzeszowPoland
  2. 2.Department of MathematicsAligarh Muslim UniversityAligarhIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-81-322-1886-9
  • Copyright Information Springer India 2014
  • Publisher Name Springer, New Delhi
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-81-322-1885-2
  • Online ISBN 978-81-322-1886-9
  • About this book