Name: Applied Summability Methods
ISBN: 978-3-319-04609-9

Authors:

M. Mursaleen ⁰

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)

Front Matter

Pages i-x

PDF
Toeplitz Matrices
- M. Mursaleen
Pages 1-11
Lambert Summability and the Prime Number Theorem
- M. Mursaleen
Pages 13-22
Summability Tests for Singular Points
- M. Mursaleen
Pages 23-29
Lototski Summability and Analytic Continuation
- M. Mursaleen
Pages 31-39
Summability Methods for Random Variables
- M. Mursaleen
Pages 41-51
Almost Summability
- M. Mursaleen
Pages 53-60
Almost Summability of Taylor Series
- M. Mursaleen
Pages 61-65
Matrix Summability of Fourier and Walsh-Fourier Series
- M. Mursaleen
Pages 67-74
Almost Convergence in Approximation Process
- M. Mursaleen
Pages 75-82
Statistical Summability
- M. Mursaleen
Pages 83-95
Statistical Approximation
- M. Mursaleen
Pages 97-110
Applications to Fixed Point Theorems
- M. Mursaleen
Pages 111-118
Back Matter

Pages 119-124

PDF

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.

Keywords

Authors and Affiliations

Department of Mathematics, Aligarh Muslim University, Aligarh, India

M. Mursaleen

Bibliographic Information

Book Title: Applied Summability Methods
Authors: M. Mursaleen
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-04609-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Softcover ISBN: 978-3-319-04608-2Published: 10 April 2014
eBook ISBN: 978-3-319-04609-9Published: 27 March 2014
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: X, 124
Topics: Sequences, Series, Summability, Number Theory, Linear and Multilinear Algebras, Matrix Theory

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Table of contents (12 chapters)

Front Matter

Back Matter

About this book

Keywords

Authors and Affiliations

Department of Mathematics, Aligarh Muslim University, Aligarh, India

Bibliographic Information

Publish with us

Buy it now

Buying options

Other ways to access

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