Multidimensional Matrix Characterization of Asymptotic Equivalent and Ideal for Double Sequences

Savas R. , Patterson R. F.

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, vol.40, no.6, pp.654-669, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 6
  • Publication Date: 2019
  • Doi Number: 10.1080/01630563.2018.1557204
  • Title of Journal : NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
  • Page Numbers: pp.654-669
  • Keywords: Asymptotically equivalent double sequences, double sequences, double ideal convergence, Pringsheim limit point, rates of convergence, statistical Limit, CONVERGENCE

Abstract

The goal of this article is to study equivalence double nonnegative sequences. To accomplish this we present a series of theorems that are similar to the following: If A is a nonnegative four dimensional summability matrix that maps bounded double sequences to and let and be admissible ideals in then the following are equivalent. If and are bounded double sequences such that and , for some , then for each m and n, for each . In addition other variations and implications shall also be presented.