Cover

Title Page

Copyright

Contents

Preface

About the Authors

About the Book

Chapter 1 Introduction and General Matrix Methods

1.1 Brief Introduction

1.2 General Matrix Methods

1.3 Exercise

References

Chapter 2 Special Summability Methods I

2.1 The Nörlund Method

2.2 The Weighted Mean Method

2.3 The Abel Method and the (C,1) Method

2.4 Exercise

References

Chapter 3 Special Summability Methods II

3.1 The Natarajan Method and the Abel Method

3.2 The Euler and Borel Methods

3.3 The Taylor Method

3.4 The Hölder and Cesàro Methods

3.5 The Hausdorff Method

3.6 Exercise

References

Chapter 4 Tauberian Theorems

4.1 Brief Introduction

4.2 Tauberian Theorems

4.3 Exercise

References

Chapter 5 Matrix Transformations of Summability and Absolute Summability Domains: Inverse-Transformation Method

5.1 Introduction

5.2 Some Notions and Auxiliary Results

5.3 The Existence Conditions of Matrix Transform Mx

5.4 Matrix Transforms for Reversible Methods

5.5 Matrix Transforms for Normal Methods

5.6 Exercise

References

Chapter 6 Matrix Transformations of Summability and Absolute Summability Domains: Peyerimhoff's Method

6.1 Introduction

6.2 Perfect Matrix Methods

6.3 The Existence Conditions of Matrix Transform Mx

6.4 Matrix Transforms for Regular Perfect Methods

6.5 Exercise

References

Chapter 7 Matrix Transformations of Summability and Absolute Summability Domains: The Case of Special Matrices

7.1 Introduction

7.2 The Case of Riesz Methods

7.3 The Case of Cesàro Methods

7.4 Some Classes of Matrix Transforms

7.5 Exercise

References

Chapter 8 On Convergence and Summability with Speed I

8.1 Introduction

8.2 The Sets (m𝝀,m𝝁), (c𝝀, c𝝁), and (c𝝀,m𝝁)

8.3 Matrix Transforms from m𝝀A into m𝝁B

8.4 On Orders of Approximation of Fourier Expansions

8.5 Exercise

References

Chapter 9 On Convergence and Summability with Speed II

9.1 Introduction

9.2 Some Topological Properties of m𝝀, c𝝀, c𝝀A and m𝝀 A

9.3 Matrix Transforms from c𝝀A into c𝝁B or m𝝁 B

9.5 Exercise

References

Index

EULA