TY  - BOOK
AU  - Mursaleen,M.
ED  - SpringerLink (Online service)
TI  - Applied Summability Methods
T2  - SpringerBriefs in Mathematics,
SN  - 9783319046099
AV  - QA292 
U1  - 515.24 23
PY  - 2014///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - mathematics
KW  - Matrix theory
KW  - Sequences (Mathematics)
KW  - Number theory
KW  - Mathematics
KW  - Sequences, Series, Summability
KW  - Number Theory
KW  - Linear and Multilinear Algebras, Matrix Theory
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/978-3-319-04609-9
ER  -