On ℐ-asymptotically lacunary statistical equivalent sequences

By Ekrem Savas. 2012

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AbstractThis paper presents the following definition, which is a natural combination of the definitions for asymptotically equivalent, ℐ-statistically limit and ℐ-lacunary statistical convergence. Let θ be a lacunary sequence; the two nonnegative sequences x=(xk) and y=(yk) are said to be ℐ-asymptotically lacunary statistical equivalent of multiple L provided that for every ϵ>0, and δ>0, {r∈N:1hr|{k∈Ir:|xkyk−L|≥ε}|≥δ}∈I (denoted by x∼SθL(I)y) and simply ℐ-asymptotically lacunary statistical equivalent if L=1.MSC:40A99, 40A05.

Subfields: Applied Mathematics, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/baeb332c03587f837e14504403fbe1484bf8ea1b