Asian Research Journal of Mathematics

Some Geometric Properties of a Generalized Difference Sequence Space Involving Lacunary Sequence

Sushomita Mohanta *

Department of Mathematics, Utkal University, Vani-Vihar, Bhubaneswar-751004, India.

*Author to whom correspondence should be addressed.

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Abstract

In this paper, we define a new generalized difference sequence space l(p, θ,Δ^m, s) involving lacunary sequence where p = (p_r) is a bounded sequence of positive real numbers with p_r > 1 for all r ∈ and s ≥ 0. Then, we examine the uniform Opial property, k-NUC property and Banach-Saks property of type p for this space.

Keywords: Difference sequence space, lacunary sequence, Luxemburg norm, uniform Opial property, Fatou property, Banach Saks of type p.

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