Displaying similar documents to “Lacunary statistical convergence and inclusion properties between lacunary methods.”

Lacunary equi-statistical convergence of positive linear operators

Hüseyin Aktuğlu, Halil Gezer (2009)

Open Mathematics

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In this paper, the concept of lacunary equi-statistical convergence is introduced and it is shown that lacunary equi-statistical convergence lies between lacunary statistical pointwise and lacunary statistical uniform convergence. Inclusion relations between equi-statistical and lacunary equi-statistical convergence are investigated and it is proved that, under some conditions, lacunary equi-statistical convergence and equi-statistical convergence are equivalent to each other. A Korovkin...

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...