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
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.
- Jincai Wang
- Suzhou University, Department of Mathematics, Suzhou, 215006 P.R. China
- Chunyan Wu
- Suzhou University, Department of Mathematics, Suzhou, 215006 P.R. China
- Received: 2009-11-02.
- Revised: 2010-01-15.
- Accepted: 2010-01-18.
