On statistical acceleration convergence of double sequences

Bipan Hazarika

doi:10.5269/bspm.v35i2.26318

Abstract

In this article the notion of statistical acceleration convergence of double sequences in Pringsheim's sense has been introduced. We prove the decompostion theorems for statistical acceleration convergence of double sequences and some theorems related to that concept have been established using the four dimensional matrix transformations. We provided some examples, where the results of acceleration convergence fails to hold for the statistical cases.

Highlights

In this case, we write st − lim x = l or −s→t l and st denotes the set of all statistically convergent sequences
The problem of acceleration convergence often occurs in numerical analysis
It is useful to study about the acceleration of convergence methods, which transform a slowly converging sequence into a new sequence, converging to the same limit faster than the original sequence

Summary

On statistical acceleration convergence of double sequences

Bipan Hazarika abstract: In this article the notion of statistical acceleration convergence of double sequences in Pringsheim’s sense has been introduced. [12,10] A real double sequence x = (xm,n) is said to be statistically convergent to the number l in Pringsheim’s sense if for each ε > 0, the set. In this case, we write st2 − lim x = l or (xk) −s→t2 l and st denotes the set of all statistically convergent double sequences. 2c = the space of all convergent in Pringsheim’s sense double sequences of real numbers. 2c = the space of all statistically convergent in Pringsheim’s sense double sequences of real numbers. [10] The sequence x = (xm,n) is said to converge at the same rate in Pringsheim’s sense as the sequence y = (ym,n), written as x ≈P y, if 0 < P − lim − inf xm,n ym,n.

Next y

Then there exists a subset