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Contractive and optimal sets in Musielak-Orlicz spaces with a smoothness condition

Denkowska A.

Opuscula Mathematica

2013

Vol. 33, no. 4

667--684

In this paper we use our recent generalization of a theorem of Jamison--Kaminska-Lewicki (characterizing one-complemented subspaces in Musielak-Orlicz sequence spaces defined by Musielak-Orlicz functions satisfying a general smoothness condition) in order to compare contractive and optimal sets in finite-dimensional Musielak-Orlicz [formula] spaces in the spirit of Kaminska-Lewicki. We also give an example illustrating the importance of the smoothness assumptions in our theorem.

On the complex locally uniform rotundity of Musielak-Orlicz sequence spaces

Wang T., Teng Y., Bian S.

Bulletin of the Polish Academy of Sciences. Mathematics

1999

Vol. 47, no 4

303-311

The concepts of complex locally uniform rotundity and complex locally uniformly rotund point are introduced and the sufficient and necessary conditions of them in Musielak-Orlicz sequence space are given.