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Bu çalışmada küme dizileri için kuvvetli asimptotik ℐ-invaryant denklik,-asimptotik ℐ-invaryant denklik, kuvvetli-asimptotik ℐ-invaryant denklik ve asimptotik ℐ-invaryant istatistiksel denklik tanımları verildi. Daha sonra, verilen bu yeni kavramlar arasındaki ilişkiler incelendi.

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Nuray et al. (2011) denoted the notions of invariant uniform density of subsets E of N , ideal invariant convergence and examined inclusion and necessity relations among ideal invariant convergence, invariant convergence and p -strongly invariant convergence. Recently, ideal invariant convergence for double set sequences introduced by Tortop and Dündar (2018) and Wijsman J2 vi -convergence for double set sequences denoted by Dündar and Pancaroğlu Akın (2020).The notion of asymptotically equivalence and some important properties of this notion investigated by some mathematicians

We investigate the notions of strongly asymptotically-equivalence, f-asymptotically-equivalence, strongly f-asymptotically-equivalence and asymptotically-statistical equivalence for sequences of sets. Also, we investigate some relationships among these concepts.