We have introduced and studied a new concept of -lacunary statistical convergence, where is an unbounded modulus. It is shown that, under certain conditions on a modulus , the concepts of lacunary strong convergence with respect to a modulus and -lacunary statistical convergence are equivalent on bounded sequences. We further characterize those for which , where and denote the sets of all -lacunary statistically convergent sequences and -statistically convergent sequences, respectively. A general description of inclusion between two arbitrary lacunary methods of -statistical convergence is given. Finally, we give an -analog of the Cauchy criterion for convergence and a Tauberian theorem for -convergence is also proved.
Vinod K. Bhardwaj. Shweta Dhawan. "Density by Moduli and Lacunary Statistical Convergence." Abstr. Appl. Anal. 2016 1 - 11, 2016. https://doi.org/10.1155/2016/9365037