σ-asymptotically lacunary statistical equivalent sequences
Ekrem Savaş ; Richard Patterson
Open Mathematics, Tome 4 (2006), p. 648-655 / Harvested from The Polish Digital Mathematics Library
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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 limr1hrk∈Ir:xσk(m)yσk(m)-L⩾∈=0 uniformly in m = 1, 2, 3, ..., (denoted by x ∼Sσ,θ y) simply S σ,8-asymptotically equivalent, if L = 1. Using this definition we shall prove S σ,8-asymptotically equivalent analogues of Fridy and Orhan’s theorems in [5] and analogues results of Das and Patel in [1] shall also be presented.

Publié le : 2006-01-01
EUDML-ID : urn:eudml:doc:269459 
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     author = {Ekrem Sava\c s and Richard Patterson},
     title = {$\sigma$-asymptotically lacunary statistical equivalent sequences},
     journal = {Open Mathematics},
     volume = {4},
     year = {2006},
     pages = {648-655},
     zbl = {1109.40002},
     language = {en},
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Ekrem Savaş; Richard Patterson. σ-asymptotically lacunary statistical equivalent sequences. Open Mathematics, Tome 4 (2006) pp. 648-655. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-006-0031-8/

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