In this paper, we define a new generalized difference sequence space l(p, θ, ∆m, s) involving lacunarysequence where p = (pr) is a bounded sequence of positive real numbers with pr >1 for all r ∈ N and s ≥ 0. Then, we examine the uniform Opial property, k-NUC property and Banach-Saksproperty of type p for this space.
Department of Mathematics, Utkal University, Vani-Vihar, Bhubaneswar-751004, India.
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