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

Agnew gave the necessary and sufficient conditions for the triangular regular matrices to yield lim supnG(An(F);D)≤lim supkG(fk;D) for all uniformly bounded real function sequences F=(fk)F=(fk). Recently, Duman studied some variants of this inequality by replacing the operator limsup with st-limsup. In this note, we present some new inequalities involving invariant means like the above mentioned results.