We have generalized the notion of statistical boundedness by introducing the concept of -statistical boundedness for scalar sequences where is an unbounded modulus. It is shown that bounded sequences are precisely those sequences which are -statistically bounded for every unbounded modulus . A decomposition theorem for -statistical convergence for vector valued sequences and a structure theorem for -statistical boundedness have also been established.
Vinod K. Bhardwaj. Shweta Dhawan. Sandeep Gupta. "Density by Moduli and Statistical Boundedness." Abstr. Appl. Anal. 2016 1 - 6, 2016. https://doi.org/10.1155/2016/2143018