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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.38 no.3 Antofagasta ago. 2019 


On a new class of generalized difference sequence spaces of fractional order defined by modulus function

1Dera Natung Govt. College, Department of Mathematics, Itanagar-791111, Arunachal Pradesh, India. e-mail :


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

Mathematics Subject Classification (2000):  46A45; 40A35; 46A80

Texto completo disponible sólo en PDF.

Full text available only in PDF format.


The author would like to express his gratitude to the anonymous referees for making necessary comments which make the paper more readable.


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Received: April 2018; Accepted: October 2018

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