Opuscula Math. 30, no. 2 (2010), 209-215

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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Cite this article as:
Jincai Wang, Chunyan Wu, On a property of ϕ-variational modular spaces, Opuscula Math. 30, no. 2 (2010), 209-215, http://dx.doi.org/10.7494/OpMath.2010.30.2.209

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