Tauberian conditions on some slowly decreasing sequences

Necessary and sufficient Tauberian conditions for weighted mean methods of summability in two-normed spaces

“…Such conditions are called Tauberian conditions and the resulting theorem is called a Tauberian theorem. Tauberian type theorems have a long history: see, for example, the book [10] and the papers [1,2,4,12,16,17].…”