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International Journal of Mathematics and Mathematical Sciences
Volume 2015, Article ID 984283, 6 pages
http://dx.doi.org/10.1155/2015/984283
Research Article

Generalized Lacunary Statistical Difference Sequence Spaces of Fractional Order

Department of Mathematics, Bozok University, Yozgat, Turkey

Received 28 April 2015; Accepted 16 June 2015

Academic Editor: Binod C. Tripathy

Copyright © 2015 Ugur Kadak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.