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Vietnam Journal of Mathematics 36:4(2008) 405-413  New Lacunary Strongly Summable Difference Sequences and $\triangle^{m}_v$- Lacunary Almost Statistical Convergence Vakeel A. Khan Abstract.  The purpose of this paper is to introduce the concept of $\triangle^{m}_v$-lacunary strongly almost convergence with respect to a sequence of moduli and $\triangle^{m}_v$- lacunary almost statistical convergence and give some relations between these two kinds of convergence. The results proved here are analogous to those by R. Colak, B. C. Tripathy and M. Et (Vietnam Journal of Mathematics {\bf 34}:2(2006) 129 -138).   2000 Mathematics Subject Classification: 40A05, 40C05, 46A45. Keywords: Difference sequence, Statistical convergence, Lacunary sequence, Sequence of moduli.

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