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- W2077889845 abstract "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 $$mathop {lim }limits_r frac{1}{{h_r }}left{ {k in I_r :left| {frac{{x_{sigma ^k (m)} }}{{y_{sigma ^k (m)} }} - L} right| geqslant in } right} = 0$$ uniformly in m = 1, 2, 3, ..., (denoted by x $$mathop sim limits^{S_{sigma ,theta } } $$ 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." @default.
- W2077889845 created "2016-06-24" @default.
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- W2077889845 date "2006-12-01" @default.
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- W2077889845 title "σ-asymptotically lacunary statistical equivalent sequences" @default.
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- W2077889845 doi "https://doi.org/10.2478/s11533-006-0031-8" @default.
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