Density by Moduli and Statistical Boundedness

Abstract

We have generalized the notion of statistical boundedness by introducing the concept of $f$-statistical boundedness for scalar sequences where $f$ is an unbounded modulus. It is shown that bounded sequences are precisely those sequences which are $f$-statistically bounded for every unbounded modulus $f$. A decomposition theorem for $f$-statistical convergence for vector valued sequences and a structure theorem for $f$-statistical boundedness have also been established.