Applied Summability Methods

  • M.┬áMursaleen

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-x
  2. M. Mursaleen
    Pages 1-11
  3. M. Mursaleen
    Pages 23-29
  4. M. Mursaleen
    Pages 41-51
  5. M. Mursaleen
    Pages 53-60
  6. M. Mursaleen
    Pages 61-65
  7. M. Mursaleen
    Pages 83-95
  8. M. Mursaleen
    Pages 97-110
  9. M. Mursaleen
    Pages 111-118
  10. Back Matter
    Pages 119-124

About this book

Introduction

This short monograph is the first book to focus exclusively on the study of summability methods, which have become active areas of research in recent years. The book provides basic definitions of sequence spaces, matrix transformations, regular matrices and some special matrices, making the material accessible to mathematicians who are new to the subject. Among the core items covered are the proof of the Prime Number Theorem using Lambert's summability and Wiener's Tauberian theorem, some results on summability tests for singular points of an analytic function, and analytic continuation through Lototski summability. Almost summability is introduced to prove Korovkin-type approximation theorems and the last chapters feature statistical summability, statistical approximation, and some applications of summability methods in fixed point theorems.

Keywords

Korovkin approximation theorems Lambert summability Lototski summability Toeplitz matrices prime number theorem statistical approximation

Authors and affiliations

  • M.┬áMursaleen
    • 1
  1. 1.Department of MathematicsAligarh Muslim UniversityAligarhIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-04609-9
  • Copyright Information M. Mursaleen 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-04608-2
  • Online ISBN 978-3-319-04609-9
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • About this book