On Wijsman asymptotically lacunary I-statistical equivalence of weight g of sequence of sets.

This paper presents the following definition which is a natural combination of the definitions of asymptotically equivalence, I-convergence, statistical limit, lacunary sequence, and Wijsman convergence of weight g; where g:N→[0,∞) is a function satisfying limn→∞ g(n)=∞ and n/g(n) →0 as n →∞ for sequence of sets. Let (X,ρ) be a metric space, θ ={kr} be a lacunary sequence and I ⊆ 2N be an admissible ideal. For any non-empty closed subsets Ak, Bk ⊆ X such that d (x, Ak > 0 and d(x, Bk) > 0 for each x ∊ X, we say that the sequences {Ak} and {Bk} are Wijsman I-asymptotically lacunary statistical equivalent of multiple L of weight g if for every ∊>0,δ>0 and for each x∊X, {r∊N:1/g(hr)∣{k∊Ir:∣ d(x,Ak)/d(x,Bk)-L∣≥∊}∣≥δ}∊I (denoted by AksLθ(IW)~g Bk). We mainly investigate their relationship and also make some observations about these classes. [ABSTRACT FROM AUTHOR]