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Journal of Convex Analysis 22 (2015), No. 3, 747--768
Copyright Heldermann Verlag 2015

Uniform Rotundity and k-Uniform Rotundity in Musielak-Orlicz-Bochner Function Spaces and Applications

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

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

We give criteria for uniform rotundity of Musielak-Orlicz-Bochner function spaces equipped with Orlicz norm are given. We also prove that, in Musielak-Orlicz-Bochner function spaces, uniform rotundity and $k$-uniform rotundity are equivalent. Moreover, we give a sufficient condition for a Musielak-Orlicz-Bochner function space to have the fixed point property.

Keywords: Musielak-Orlicz-Bochner function spaces, uniform rotundity, k-uniform rotundity, Orlicz norm, fixed point.

MSC: 46E30, 46B20

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