Abstract
In this paper, we introduce and investigate relationship among s -statistically convergent and [,, ]s I -statistically convergent, r r I V 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
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.
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