More Properties of the $$(M, \lambda _n)$$ Method and Cauchy Multiplication of Certain Summable Series

Abstract

In the present chapter, more properties of the \((M, \lambda _n)\) method are established. For instance, it is proved that the set \(\mathcal {M}\) of all \((M, \lambda _n)\) methods is an ordered abelian semigroup and there are infinite chains of \((M, \lambda _n)\) methods from \(\mathcal {M}\). A few results on the Cauchy multiplication of certain summable series are also proved.