Further Results on (Δ_s^j,f)-Lacunary Statistical Convergence of Double Sequences of order α

Abstract

This paper defines the space S_(θ_uv)^α (Δ_s^j,f), encompassing all sequences that are (Δ_s^j,f)-lacunary statistically convergent of order α, utilizing an unbounded modulus function f, a double lacunary sequence θ_uv={(k_u,l_v )}, a generalized difference operator Δ_s^j, and a real number α ∈ (0,1]. Additionally, the space ω_(θ_uv)^α (Δ_s^j,f) is introduced to include all sequences that are strongly (Δ_s^j,f)-lacunary summable of order α. The paper investigates properties associated with these spaces, and under specific conditions, inclusion relations between the spaces S_(θ_uv)^α (Δ_s^j,f) and ω_(θ_uv)^α (Δ_s^j,f) are established.

Keywords

• lacunary sequences
• lacunary statistical convergence
• Modulus function

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