On the generalizations of some factors theorems for infinite series and fourier series

Quite recently, Bor [Quaest. Math. (doi.org/10.2989/16073606.2019.1578836, in press)] has proved a new result on weighted arithmetic mean summability factors of non decreasing sequences and application on Fourier series. In this paper, we establish a general theorem dealing with absolute matrix summability by using an almost increasing sequence and normal matrices in place of a positive non-decreasing sequence and weighted mean matrices, respectively. So, we extend his result to more general cases.

A general matrix application of convex sequences to Fourier series

By using a convex sequence Bor [H. Bor, Local properties of factored Fourier series, Appl. Math. Comp. 212 (2009) 82-85] has obtained a result dealing with local property of factored Fourier series for weighted mean summability. The purpose of this paper is to extend this result to more general cases by taking normal matrices in place of weighted mean matrices.

Simple Conditions for Matrices to be Bounded Operators on lp

The two theorems proved yield simple yet reasonably general conditions for triangular matrices to be bounded operators on lp. The theorems are applied to Nörlund and weighted mean matrices.

The spectra of weighted mean operators on bν0

In a series of papers, the author has previously investigated the spectra and fine spectra for weighted mean matrices, considered as bounded operators over various sequence spaces. This paper examines the spectra of weighted mean matrices as operators over bνv0, the space of null sequences of bounded variation.