In this article, we aim to define ℐ 2 (풮) -summability and ℐ 2 (풮 θ p , r ) -summability, and obtain interesting relationships among these by imposing certain conditions on p and r. Finally, we show that the space ℐ 2 (풮 θ p , r (G , B , Y)) ∩ l ∞ 2 (V) is a closed subspace of l ∞ 2 (V) .