Convergence Methods for Double Sequences and Applications

  • M. Mursaleen
  • S.A. Mohiuddine

Table of contents

  1. Front Matter
    Pages I-IX
  2. M. Mursaleen, S. A. Mohiuddine
    Pages 17-39
  3. M. Mursaleen, S. A. Mohiuddine
    Pages 41-61
  4. M. Mursaleen, S. A. Mohiuddine
    Pages 63-77
  5. M. Mursaleen, S. A. Mohiuddine
    Pages 79-97
  6. M. Mursaleen, S. A. Mohiuddine
    Pages 117-132
  7. M. Mursaleen, S. A. Mohiuddine
    Pages 133-148
  8. M. Mursaleen, S. A. Mohiuddine
    Pages 149-166
  9. Back Matter
    Pages 167-171

About this book

Introduction

This book exclusively deals with the study of almost convergence and statistical convergence of double sequences. The notion of “almost convergence” is perhaps the most useful notion in order to obtain a weak limit of a bounded non-convergent sequence. There is another notion of convergence known as the “statistical convergence”, introduced by H. Fast, which is an extension of the usual concept of sequential limits. This concept arises as an example of “convergence in density” which is also studied as a summability method. Even unbounded sequences can be dealt with by using this method.

The book also discusses the applications of these non-matrix methods in approximation theory. Written in a self-contained style, the book discusses in detail the methods of almost convergence and statistical convergence for double sequences along with applications and suitable examples. The last chapter is devoted to the study convergence of double series and describes various convergence tests analogous to those of single sequences. In addition to applications in approximation theory, the results are expected to find application in many other areas of pure and applied mathematics such as mathematical analysis, probability, fixed point theory and statistics.

Keywords

Convergence of double series Double sequences Korovkin type approximation theorems Statistical convergence

Authors and affiliations

  • M. Mursaleen
    • 1
  • S.A. Mohiuddine
    • 2
  1. 1.Department of MathematicsAligarh Muslim UniversityAligarhIndia
  2. 2.Department of MathematicsKing Abdulaziz UniversityJeddahSaudi Arabia

Bibliographic information

  • DOI https://doi.org/10.1007/978-81-322-1611-7
  • Copyright Information Springer India 2014
  • Publisher Name Springer, New Delhi
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-81-322-1610-0
  • Online ISBN 978-81-322-1611-7
  • About this book