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Displaying similar documents to “Asymptotic equivalence and summability.”

σ-asymptotically lacunary statistical equivalent sequences

Ekrem Savaş, Richard Patterson (2006)

Open Mathematics

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This paper presents the following definitions which is a natural combination of the definition for asymptotically equivalent, statistically limit, lacunary sequences, and σ-convergence. Let ϑ be a lacunary sequence; Two nonnegative sequences [x] and [y] are S σ,8-asymptotically equivalent of multiple L provided that for every ε > 0 lim r 1 h r k ∈ I r : x σ k ( m ) y σ k ( m ) - L ⩾ ∈ = 0 uniformly in m = 1, 2, 3, ..., (denoted by x ∼ S σ , θ y) simply S σ,8-asymptotically equivalent, if L = 1. Using this definition we shall prove S σ,8-asymptotically...