On Cauchy-type functional equations.

Elhoucien, Elqorachi; Akkouchi, Mohamed

Displaying similar documents to “On Cauchy-type functional equations.”

Potential theory of quasiminimizers.

Kinnunen, Juha, Martio, Olli (2003)

Annales Academiae Scientiarum Fennicae. Mathematica

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Generalizations of Hölder's inequality.

Cheung, Wing-Sum (2001)

International Journal of Mathematics and Mathematical Sciences

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Dichotomies for $𝐂_{0} (X)$ and $𝐂_{b} (X)$ spaces

Szymon Głąb, Filip Strobin (2013)

Czechoslovak Mathematical Journal

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Jachymski showed that the set $\{(x, y) \in 𝐜_{0} \times 𝐜_{0} : {(\sum_{i = 1}^{n} α (i) x (i) y (i))}_{n = 1}^{\infty} is bounded\}$ is either a meager subset of $𝐜_{0} \times 𝐜_{0}$ or is equal to $𝐜_{0} \times 𝐜_{0}$ . In the paper we generalize this result by considering more general spaces than $𝐜_{0}$ , namely $𝐂_{0} (X)$ , the space of all continuous functions which vanish at infinity, and $𝐂_{b} (X)$ , the space of all continuous bounded functions. Moreover, we replace the meagerness by $σ$ -porosity.