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On a property of phi-variational modular spaces

Wang J., Wu C.

Opuscula Mathematica

2010

Vol. 30, no. 2

209-215

Maligranda pointed out whether condition (B.1) is satisfied in the variational modular space X*ρ is an open problem. We will answer this open problem in X*ρ', a subspace of X*ρ. As a consequence this modular space X*ρ' can be F-normed.

A note on fi-variational modular spaces

Wang J. C., Hudzik H.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2001

[Z] 41

93-98

A criterion for local boundedness of the variational modular space X is given. Local boundedness of X guarantee that the modular pstatisfies condition (B.1). In consequence such modular spaces can be F-normed.