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Vietnam Journal of Mathematics 34:2(2006) 129-138

Lacunary Strongly Summable Sequences and q-Lacunary Almost Statistical Convergence 

Rifat Çolak, B. C. Tripathy, and Mikâil Et

Abstract.  A lacunary sequence is an increasing sequence θ = (k_r) of positive integers such that k₀ = 0 and k_r – k_r-l -> ∞ as r -> ∞. A sequence x = (x_k) is called q-lacunary almost statistical convergent to ξ provided that for each ε > 0, lim_r(k_r - k_r-1) ^-1 the number of k : k_r-1.

2000 Mathematics Subject Classification: 40A05, 40C05, 46A45.

Keywords: Statistical convergence, lacunary sequence, Orlicz function, almost convergence.

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Published by Springer since January 2013