A-Sequence Spaces in 2-Normed Space Defined by Ideal Convergence and an Orlicz Function

and Applied Analysis 3 of positive real numbers. By S 2 − X , we denote the space of all sequences defined over X, ‖·, ·‖ . Now we define the following sequence spaces: W ( M,Δ, p, ‖, ·, ‖ ⎧ ⎪⎨ ⎪⎩ x ∈ S 2 −X : ∀ε > 0 { n ∈ : ∞ ∑ k 1 ank [ M (∥ ∥ ∥ ∥ Δxk − L ρ , z ∥ ∥ ∥ ∥ )]pk ≥ ε } ∈ I for some ρ > 0, L ∈ X and each z ∈ X ⎫ ⎪⎬ ⎪⎭ , W 0 ( A,M,Δ, p, ‖, ·, ‖ ⎧ ⎪⎨ ⎪⎩ x ∈ S 2 −X : ∀ε > 0 { n ∈ : ∞ ∑ k 1 ank [ M (∥ ∥ ∥ ∥ Δxk ρ , z ∥ ∥ ∥ ∥ )]pk ≥ ε } ∈ I for some ρ > 0, and each z ∈ X ⎫ ⎪⎬ ⎪⎭ , W∞ ( A,M,Δ, p, ‖, ·, ‖ ⎧ ⎪⎨ ⎪⎩ x ∈ S 2 −X : ∃K > 0 s.t. sup n∈ ∞ ∑ k 1 ank [ M (∥ ∥ ∥ ∥ Δxk ρ , z ∥ ∥ ∥ ∥ )]pk ≤ K for some ρ > 0, and each z ∈ X ⎫ ⎪⎬ ⎪⎭ , W ∞ ( A,M,Δ, p, ‖, ·, ‖ { x ∈ S 2 −X : ∃K > 0, s.t. { n ∈ : ∞ ∑ k 1 ank [ M (∥ ∥ ∥ ∥ Δxk ρ , z ∥ ∥ ∥ ∥ )]pk ≥ K } ∈ I for some ρ > 0, and each z ∈ X }