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

Abstract

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