p-Summable Vector-Valued Sequence Spaces in Non-Archimedean 2-Normed Spaces

Let (X, ‖., .‖) be a non-Archimedean 2-normed spaces. In this paper, we construct p-summable vector-valued sequence spaces in non-Archimedean 2-normed spaces ℓ p (X) for 1 ≤ p ≤ ∞. Futhermore, we show that ℓ p (X) is a non-Archimedean 2-semi-normed spaces and we also give some inclusion relations on ℓ p (X).