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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Abstract

YAYING, Taja. On a new class of generalized difference sequence spaces of fractional order defined by modulus function. Proyecciones (Antofagasta) [online]. 2019, vol.38, n.3, pp.485-497. ISSN 0716-0917.  http://dx.doi.org/10.22199/issn.0717-6279-2019-03-0031.

Recently Baliarsingh and Dutta [11], [12] introduced the fractional difference operator Δα , defined by Δα(xk) = and defined new classes of generalized difference sequence spaces of fractional order X(Γ, Δα, u) where X = {𝓁∞, c, c0} . More recently, Kadak [21] studied strongly Cesàro and statistical difference sequence space of fractional order involving lacunary sequences using the fractional difference operator

is is any fixed sequence of positive real or complex numbers.

Following Baliarsingh and Dutta [11], [12] and Kadak [21], we introduce paranormed difference sequence spaces of fractional order involving lacunary sequence, θ and modulus function, f. We investigate topological structures of these spaces and examine various inclusion relations.

Keywords : Difference operator; Paranormed sequence; Lacunary sequence; Modulus function; 46A45; 40A35; 46A80.

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