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Summability Theory And Its Applications
Author(s): Feyzi Basar
Editor(s): Rifat Çolak
eISBN: 978-1-60805-252-3   
ISBN: 978-1-60805-420-6   
Indexed in: Scopus
Chapter PDF Price: US $15

Matrix Transformations in Sequence Spaces

Author(s): Feyzi Basar
Chapter DOI: 10.2174/978160805452311201010033
Page: 33-50 (18)

In this chapter, the matrix transformations in sequence spaces are studied and the characterizations of the classes of Schur, Kojima and Toeplitz matrices together with their versions for the series-to-sequence, sequence-to-series and series-to-series matrix transformations are given.
Matrix transformations between sequence spaces, ordinary, absolute and strong summability, KOjima-Schur theorem, Silverman-Toeplitz theorem, Schur's theorem, algebra, normed and Banach algebra, characteristic of a matrix, sequence-to-sequence, series-to-sequence, series-to-series and sequence-to-series matrix transformations, dual summability methods, arithmetics, Cesàro, Euler, Riesz and Nörlund means, Taylor, Ar, Hausdor, Borel and Abel matrices.