Generalized lacunary statistical difference sequence spaces of fractional order (Q1751400)

Summary: We generalize the lacunary statistical convergence by introducing the generalized difference operator \(\Delta_\nu^\alpha\) of fractional order, where \(\alpha\) is a proper fraction and \(\nu = (\nu_k)\) 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.