Some Geometric Properties of a New Difference Sequence Space Involving Lacunary Sequences

In this paper, we define a new generalized difference sequence space involving lacunary sequence. Then, we examine k-NUC property and property (β) for this space and also show that it is not rotund where p = (pr) is a bounded sequence of positive real numbers with pr ≥ 1 for all r ∈ ℕ.