Overview
- 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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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.
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Table of contents (12 chapters)
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Front Matter
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Back Matter
Authors and Affiliations
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)
Copyright Information: M. Mursaleen 2014
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