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A Generalization of a Theorem of Móricz and Rhoades on Weighted Means

100%

Natarajan P. N.

Commentationes Mathematicae

2012

tom 52

nr 1

In this paper,we prove a theorem which gives an equivalent formulation of summability by weighted mean methods. The result of Hardy [1] and that of Móricz and Rhoades [2] are special cases of this theorem. In this context, it is important to note that the result of Móricz and Rhoades is valid even without the assumption \(\frac{p_n}{P_n}\to0\) as \(n\to\infty\).

Semigroups of transformations restricted by an equivalence

100%

Mendes-Gonçalves S., Sullivan R.

Open Mathematics

2010

tom 8

nr 6

1120-1131

Suppose σ is an equivalence on a set X and let E(X, σ) denote the semigroup (under composition) of all α: X → X such that σ ⊆ α ∘ α −1. Here we characterise Green’s relations and ideals in E(X, σ). This is analogous to recent work by Sullivan on K(V, W), the semigroup (under composition) of all linear transformations β of a vector space V such that W ⊆ ker β, where W is a fixed subspace of V.

Ograniczanie wyników

1 Commentationes Mathematicae

1 Open Mathematics

1 Mendes-Gonçalves S.

1 Natarajan P. N.

1 Sullivan R.

1 2012

1 2010

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A Generalization of a Theorem of Móricz and Rhoades on Weighted Means

Semigroups of transformations restricted by an equivalence