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Generalized Lacunary Statistical Difference Sequence Spaces of Fractional Order

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  • Ugur Kadak

Abstract

We generalize the lacunary statistical convergence by introducing the generalized difference operator of fractional order, where is a proper fraction and is any fixed sequence of nonzero real or complex numbers. We study some properties of this operator and investigate the topological structures of related sequence spaces. Furthermore, we introduce some properties of the strongly Cesaro difference sequence spaces of fractional order involving lacunary sequences and examine various inclusion relations of these spaces. We also determine the relationship between lacunary statistical and strong Cesaro difference sequence spaces of fractional order.

Suggested Citation

  • Ugur Kadak, 2015. "Generalized Lacunary Statistical Difference Sequence Spaces of Fractional Order," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2015, pages 1-6, October.
    • Handle: RePEc:hin:jijmms:984283
    DOI: 10.1155/2015/984283
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    References listed on IDEAS

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    1. Baliarsingh, P. & Dutta, S., 2015. "On the classes of fractional order difference sequence spaces and their matrix transformations," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 665-674.
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    Cited by:

    1. Ibrahim S. Ibrahim & María C. Listán-García, 2024. "A New Notion of Convergence Defined by The Fibonacci Sequence: A Novel Framework and Its Tauberian Conditions," Mathematics, MDPI, vol. 12(17), pages 1-13, August.

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