Applied Summability Methods
1st Edition
Published on 27. March 2014
X, 124 pages
978-3-319-04609-9 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Product notice
Reflowable
Illustrations
X, 124 p.
File size
1,40 MB
ISBN-13
978-3-319-04609-9 (9783319046099)
DOI
10.1007/978-3-319-04609-9
Schweitzer Classification
Other editions
Additional editions
Content
Toeplitz Matrices.- Lambert Summability and the Prime Number Theorem.- Summability Tests for Singular Points.- Lototski Summability and Analytic Continuation.- Summability Methods for Random Variables.- Almost Summability.- Almost Summability of Taylor Series.- Matrix Summability of Fourier and Walsh-Fourier Series.- Almost Convergence in Approximation Process.- Statistical Summability.- Statistical Approximation.- Applications to fixed point theorems.- Bibliography.- Index.
