Abstract
In this paper we introduce some new double difference lacunary sequence spaces using Orlicz functions, generalized double difference sequences and a two-valued measure μ in 2-normed spaces, and we also examine some of their properties.
Highlights
The notion of summability of single sequences with respect to a two-valued measure was introduced by Connor [, ] as a very interesting generalization of statistical convergence which was defined by Fast [ ]
The study of Orlicz sequence spaces was initiated with a certain specific purpose in Banach space theory
Lindenstrauss and Tzafriri [ ] investigated Orlicz sequence spaces in more detail and they proved that every Orlicz sequence space lM contains a subspace isomorphic to lp ( ≤ p < ∞)
Summary
The notion of summability of single sequences with respect to a two-valued measure was introduced by Connor [ , ] as a very interesting generalization of statistical convergence which was defined by Fast [ ]. Very recently Das and Bhunia investigated the summability of double sequences of real numbers with respect to a twovalued measure and made many interesting observations [ ]. In [ ], Das and Savaş et al introduced some generalized double difference sequence spaces using summability with respect to a two-valued measure and an Orlicz function in -normed spaces which have a unique non-linear structure. In a natural way, we first define statistical convergence for double sequences in -normed spaces using a two-valued measure and prove some interesting theorems. Let K ⊆ N × N and let K(k, l) be the cardinality of the set {(m, n) ∈ K : m ≤ k, n ≤ l}
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