Orlicz–Pettis Theorem through Summability Methods

A Generalization Theorem Covering Many Absolute Summability Methods

A general theorem concerning many absolute summability methods is proved. 2000 Mathematics Subject Classification. 40F05, 40G05, 40D15, 40D25.

Absolute matrix summability methods

A Constructive Study of Landau's Summability Theorem

A summability theorem of Landau, which classically is a simple consequence of the uniform boundedness theorem, is examined within Bishop-style constructive mathematics. It is shown that the original theorem is nonconstructive, and that a natural weakening of the theorem is constructively equivalent to Ishihara’s principle BD-N. The paper ends with a number of results that, while not as strong a...

On absolute matrix summability methods

On Absolute Matrix Summability Methods

We have proved a theorem on |T, p n | k summability methods. This theorem includes a known theorem.