Some inequalities between functionals related to generalized limits

Abstract

Recall that A-statistical core theorem determines a class of regular matrices for which lim sup(T x) ≤ stA − lim sup x for all x ∈ m. The main object of this paper is to study an inequality between functionals which is sharper than that of the A-statistical core theorem. We also study the relationship between these functionals and some generalized limits which are called SA-limits and A-Banach limits.