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Journal of Convex Analysis 21 (2014), No. 2, 477--494
Copyright Heldermann Verlag 2014

Midpoint Locally Uniform Rotundity of Musielak-Orlicz-Bochner Function Spaces Endowed with the Orlicz Norm

Shaoqiang Shang
Dept. of Mathematics, Northeast Forestry University, Harbin 150040, P. R. China

Yunan Cui
Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, P. R. China

Yongqiang Fu
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P. R. China

The criteria for midpoint locally uniform rotundity in the classical Orlicz function spaces have been given already. However, because of the complicated structure of Musielak-Orlicz-Bochner function spaces, up to now the criteria for midpoint locally uniform rotundity have not been discussed yet. In this paper, criteria for midpoint locally uniform rotundity of Musielak-Orlicz-Bochner function spaces equipped with Orlicz norm are given.

Keywords: Strongly extreme point, midpoint locally uniformly rotund, Musielak-Orlicz-Bochner function spaces, Orlicz norm.

MSC: 46E30, 46B20

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