On two new types of statistical convergence and a summability method - doi: 10.4025/actascitechnol.v36i1.16206

Hemen Dutta,Iqbal Hamzah Jebril,Bokka Surender Reddy

doi:10.4025/16206

Abstract

In this paper, we introduce and investigate relationship among I-statistically Delta_r^s -convergent, I-lambda-statistically Delta_r^s-convergent and I-[V, lambda, Delta_r^s]-summable sequences respectively over normed linear spaces

Highlights

The idea of convergence of a real sequence had been extended to statistical convergence by Fast (1951) and can be found in Schoenberg (1959) If N denotes the set of natural numbers and K N K (m, n) denotes the cardinality of K [m, n]
As a generalization of statistical convergence, the notion of ideal convergence was introduced first by Kostyrko et al (2000/2001). This was further studied in topological spaces by Lahiri and Das (2005), Das et al (2008) and many others
Introduced and studied the idea of convergence as an extension of the [V, ] summability introduced by Leindler (1965). statistical convergence is a special case of more general

Summary

Introduction

The idea of convergence of a real sequence had been extended to statistical convergence by Fast (1951) and can be found in Schoenberg (1959) If N denotes the set of natural numbers and K N K (m, n) denotes the cardinality of K [m, n]. As a generalization of statistical convergence, the notion of ideal convergence was introduced first by Kostyrko et al (2000/2001). This was further studied in topological spaces by Lahiri and Das (2005), Das et al (2008) and many others. The notion was further generalized by Et and Çolak (1995) by introducing the spaces s , c s and c0 s. Another type of generalization of the difference sequence spaces is due to Tripathy and. Tripathy et al (2005) generalized the above notions and unified these as follows: Let r, s be non- negative integers, for Z a given sequence space we have.

S rs

Conclusion