On a theorem of W. Meyer-König and H. Tietz (Q2368364)

Summary: Let \((u_n)\) be a sequence of real numbers and let \(L\) be an additive limitable method with some property. We prove that if the classical control modulo of the oscillatory behavior of \((u_n)\) belonging to some class of sequences is a Tauberian condition for \(L\), then convergence or subsequential convergence of \((u_n)\) out of \(L\) is recovered depending on the conditions on the general control modulo of the oscillatory behavior of different order.