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Acta Mathematica Vietnamica

ON SOME GENERALIZED NEW TYPE DIFFERENCE SEQUENCE SPACES DEFINED BY A MODULUS FUNCTION

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Abstract

The idea of difference sequence spaces were defined by Kizmaz [6] and generalized by Et and Ҫolak [3]. Later Tripathy et al. [16] introduced the notion of the new difference operator $\Delta_m^nx_k$ for fixed $n, m \in \mathbb N$. In this paper we introduce some new type difference sequence spaces defined by a modulus function and the new concept of statistical convergence. We give various properties and inclusion relations on these new type difference sequence spaces.