Sequence spaces defined via Euler method and matrix transformations

A blend of matrix summability and Euler summability transformation methods is used to define Lacunary sequence spaces defined over n-normed space. Then we present the properties of this space and finally, some inclusion relations are presented.

A new factor theorem on absolute matrix summability method

In this paper, we have a new matrix generalization with absolute matrix summability factor of an infinite series by using quasi-β-power increasing sequences. That theorem also includes some new and known results dealing with some basic summability methods

Least-squares community extraction in feature-rich networks using similarity data

We explore a doubly-greedy approach to the issue of community detection in feature-rich networks. According to this approach, both the network and feature data are straightforwardly recovered from the underlying unknown non-overlapping communities, supplied with a center in the feature space and intensity weight(s) over the network each. Our least-squares additive criterion allows us to search for communities one-by-one and to find each community by adding entities one by one. A focus of this paper is that the feature-space data part is converted into a similarity matrix format. The similarity/link values can be used in either of two modes: (a) as measured in the same scale so that one may can meaningfully compare and sum similarity values across the entire similarity matrix (summability mode), and (b) similarity values in one column should not be compared with the values in other columns (nonsummability mode). The two input matrices and two modes lead us to developing four different Iterative Community Extraction from Similarity data (ICESi) algorithms, which determine the number of communities automatically. Our experiments at real-world and synthetic datasets show that these algorithms are valid and competitive.

Some Problems on Approximations of Functions (Signals) in Matrix Summability of Legendre Series

In this paper, we prove a main theorem dealing the matrix summability of Legendre series using non-negative monotonic non-increasing sequences of function. This paper is more general than [9], [12] and [22].

Sequence spaces defined via Euler method and matrix transformations

A blend of matrix summability and Euler summability transformation methods is used to define Lacunary sequence spaces defined over n-normed space. Then we present the properties of this space and finally, some inclusion relations are presented.

Trigonometric approximation of functions $f(x,y)$ of generalized Lipschitz class by double Hausdorff matrix summability method

In this paper, we establish a new estimate for the degree of approximation of functions $f(x,y)$ f ( x , y ) belonging to the generalized Lipschitz class $Lip ((\xi _{1}, \xi _{2} );r )$ L i p ( ( ξ 1 , ξ 2 ) ; r ) , $r \geq 1$ r ≥ 1 , by double Hausdorff matrix summability means of double Fourier series. We also deduce the degree of approximation of functions from $Lip ((\alpha ,\beta );r )$ L i p ( ( α , β ) ; r ) and $Lip(\alpha ,\beta )$ L i p ( α , β ) in the form of corollary. We establish some auxiliary results on trigonometric approximation for almost Euler means and $(C, \gamma , \delta )$ ( C , γ , δ ) means.

A new result on the quasi power increasing sequences

This paper presents a theorem dealing with absolute matrix summability of infinite series. This theorem has been proved taking quasi β-power increasing sequence instead of almost increasing sequence.