Table of Contents
Preface ixAbout the Authors xiAbout the Book xiii
1 Introduction and General Matrix Methods 11.1 Brief Introduction 11.2 General Matrix Methods 21.3 Exercise 16References 19
2 Special Summability Methods I 212.1 The Nörlund Method 212.2 The Weighted Mean Method 292.3 The Abel Method and the (C,1) Method 342.4 Exercise 44References 45
3 Special Summability Methods II 473.1 The Natarajan Method and the Abel Method 473.2 The Euler and Borel Methods 533.3 The Taylor Method 593.4 The Hölder and Cesàro Methods 623.5 The Hausdorff Method 643.6 Exercise 73References 74
4 Tauberian Theorems 754.1 Brief Introduction 754.2 Tauberian Theorems 754.3 Exercise 83References 84
5 Matrix Transformations of Summability and Absolute Summability Domains: Inverse-Transformation Method 855.1 Introduction 855.2 Some Notions and Auxiliary Results 875.3 The Existence Conditions of Matrix Transform Mx 915.4 Matrix Transforms for Reversible Methods 955.5 Matrix Transforms for Normal Methods 1025.6 Exercise 107References 109
6 Matrix Transformations of Summability and Absolute Summability Domains: Peyerimhoff’s Method 1136.1 Introduction 1136.2 Perfect Matrix Methods 1136.3 The Existence Conditions of Matrix Transform Mx 1176.4 Matrix Transforms for Regular Perfect Methods 1216.5 Exercise 127References 129
7 Matrix Transformations of Summability and Absolute Summability Domains: The Case of Special Matrices 1317.1 Introduction 1317.2 The Case of Riesz Methods 1317.3 The Case of Cesàro Methods 1397.4 Some Classes of Matrix Transforms 1487.5 Exercise 151References 154
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 mAλ into mBμ
8.4 On orders of approximation of Fourier expansions
8.5 Exercises
References
9 On Convergence and Summability with Speed II
9.1 Introduction
9.2 Some topological properties of mλ, cλ, cAλ and mAλ
9.3 Matrix transforms from cAλ into cBμ or mBμ
9.4 Exercises
References