Savaş, Ekrem2020-11-212020-11-2120172008-18982008-1901https://doi.org/10.22436/jnsa.010.06.01https://hdl.handle.net/11467/4064This paper presents the following definition which is a natural combination of the definition for asymptotically equivalent of order alpha, where 0 < alpha <= 1, I-statistically limit, and I-lacunary statistical convergence for sequences of sets. Let (X, rho) be a metric space and theta be a lacunary sequence. For any non-empty closed subsets A(k), B-k subset of X such that d(x, A(k)) > 0 and d(x, B-k) > 0 for each x is an element of X, we say that the sequences {A(k)} and {B-k} are Wijsman asymptotically I-lacunary statistical equivalent of order alpha to multiple L, where 0 < alpha <= 1, provided that for each epsilon > 0 and each x is an element of X, {r is an element of N : 1/h(r)(alpha)|{k is an element of I-r : |d(x; A(k),B-k)- L| >= (sic) }| >= delta} is an element of I, (denoted by {A(k)} (s theta L(Iw)alpha) similar to {B-k}) and simply asymptotically I-lacunary statistical equivalent of order alpha if L = 1. In addition, we shall also present some inclusion theorems. The study leaves some interesting open problems. (C) 2017 All rights reserved.eninfo:eu-repo/semantics/openAccessAsymptotical equivalentsequences of setsideal convergenceWijsman convergenceI-statistical convergenceI-lacunary statistical convergencestatistical convergence of order alphaArticle10628602867N/AWOS:00040757730000110.22436/jnsa.010.06.01