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Applied Summability Methods

  • Book
  • © 2014

Overview

Authors:
  1. M. Mursaleen

    1. Department of Mathematics, Aligarh Muslim University, Aligarh, India

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  • Focuses exclusively on the study of summability methods and their applications
  • Features self-contained chapters appropriate for researchers and graduate students
  • Includes topics such as proof of the prime number theorem using Lambert's summability and Wiener's Tauberian theorem
  • Includes supplementary material: sn.pub/extras

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-x
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  2. Toeplitz Matrices

    • M. Mursaleen
    Pages 1-11

  3. Lambert Summability and the Prime Number Theorem

    • M. Mursaleen
    Pages 13-22

  4. Summability Tests for Singular Points

    • M. Mursaleen
    Pages 23-29

  5. Lototski Summability and Analytic Continuation

    • M. Mursaleen
    Pages 31-39

  6. Summability Methods for Random Variables

    • M. Mursaleen
    Pages 41-51

  7. Almost Summability

    • M. Mursaleen
    Pages 53-60

  8. Almost Summability of Taylor Series

    • M. Mursaleen
    Pages 61-65

  9. Matrix Summability of Fourier and Walsh-Fourier Series

    • M. Mursaleen
    Pages 67-74

  10. Almost Convergence in Approximation Process

    • M. Mursaleen
    Pages 75-82

  11. Statistical Summability

    • M. Mursaleen
    Pages 83-95

  12. Statistical Approximation

    • M. Mursaleen
    Pages 97-110

  13. Applications to Fixed Point Theorems

    • M. Mursaleen
    Pages 111-118

  14. Back Matter

    Pages 119-124
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, Aligarh Muslim University, Aligarh, India

    M. Mursaleen

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