Density by moduli and statistical boundedness (Q1669214)

Summary: 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.