Opuscula Math. 30, no. 2 (2010), 209-215
http://dx.doi.org/10.7494/OpMath.2010.30.2.209

Opuscula Mathematica

# On a property of ϕ-variational modular spaces

Jincai Wang
Chunyan Wu

Abstract. Maligranda pointed out whether condition (B.1) is satisfied in the variational modular space $$X_{\rho}^{*}$$ is an open problem. We will answer this open problem in $$X_{\rho}^{*\prime}$$, a subspace of $$X_{\rho}^{*}$$. As a consequence this modular space can $$X_{\rho}^{*\prime}$$ be $$F$$-normed.

Keywords: condition (B.1), modular, $$\phi$$ -function, $$\phi$$ -variation.

Mathematics Subject Classification: 46A80, 46E30.

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