f-Asymptotically I_2^σθ-Equivalence for Double Set Sequences

Recently, Akin, Dundar and Ulusu defined and studied asymptotically lacunary I-invariant statistical equivalence for sequences of sets defined by a modulus function [N. P. Akin, E. Dundar and U.Ulusu, Asymptotically Lacunary I-Invariant Statistical Equivalence of Sequences of Set Defined By A Modulus Function, Sakarya Univ. J. Sci. 22(6) (2018)]. In this study, first, we present the concepts of strongly asymptotically I_2^σθ-equivalence, f-asymptotically I_2^σθ-equivalence, strongly f-asymptotically I_2^σθ-equivalence for double sequences of sets. Then, we investigate some properties and relationships among this new concepts. After, we present asymptotically I_2^σθ-statistical equivalence for double sequences of sets. Also we investigate relationships between asymptotically I_2^σθ-statistical equivalence and strongly f-asymptotically I_2^σθ-equivalence.