Some new inequalities related to the invariant means and uniformly bounded function sequences (Q878989)

In 1930, R. P. Agnew characterized a class of triangular matrices \(A=\left( a_{nk}\right) \) with the property that the inequality \[ \limsup_{n}\sup_{x\in D}\sum_{k}a_{nk}f_{k}\left( x\right) \leq \limsup_{k}\sup_{x\in D}f_{k}\left( x\right) \] holds for function sequences \(\left( f_{k}\right) \) uniformly bounded on \(D.\) In the paper under review, some inequalities of this type are proved in the context of invariant means and statistical convergence.