Sequence spaces defined via Euler method and matrix transformations

Pranav Sharma

doi:10.22199/issn.0717-6279-5119

Abstract

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.

Highlights

Accelerated convergence techniques are useful in computer science especially in making graphics and to find eigenvalues and eigenvectors of dynamical systems
We study certain properties of a class of sequences over an n-normed space using Musielak-Orlicz function
Sequence spaces defined by Orlicz function have been introduced and their different properties have been investigated by Tripathy and Mahanta [14, 15]

Summary

Introduction

Accelerated convergence techniques are useful in computer science especially in making graphics and to find eigenvalues and eigenvectors of dynamical systems. For a positive real q and a non negative integer n, the Euler transform Let x = (xn) be a sequence of scalars, for n ≥ 1 we will denote by Nn(x) the difference Enq (x) − Enq−1(x), where Enq is defined as above. We study certain properties of a class of sequences (defined by using Euler transform) over an n-normed space using Musielak-Orlicz function.

Results

Conclusion