Displaying similar documents to “Double Sequence Spaces Definedby a Sequence of Modulus Functions over n -normed Spaces”

Two valued measure and some new double sequence spaces in 2 -normed spaces

Pratulananda Das, Ekrem Savaş, Santanu Bhunia (2011)

Czechoslovak Mathematical Journal

Similarity:

The purpose of this paper is to introduce some new generalized double difference sequence spaces using summability with respect to a two valued measure and an Orlicz function in 2 -normed spaces which have unique non-linear structure and to examine some of their properties. This approach has not been used in any context before.

σ-asymptotically lacunary statistical equivalent sequences

Ekrem Savaş, Richard Patterson (2006)

Open Mathematics

Similarity:

This paper presents the following definitions which is a natural combination of the definition for asymptotically equivalent, statistically limit, lacunary sequences, and σ-convergence. Let ϑ be a lacunary sequence; Two nonnegative sequences [x] and [y] are S σ,8-asymptotically equivalent of multiple L provided that for every ε > 0 lim r 1 h r k ∈ I r : x σ k ( m ) y σ k ( m ) - L ⩾ ∈ = 0 uniformly in m = 1, 2, 3, ..., (denoted by x ∼ S σ , θ y) simply S σ,8-asymptotically equivalent, if L = 1. Using this definition we shall prove S σ,8-asymptotically...