Density by Moduli and Statistical Boundedness

Abstract EN

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.