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
sqshang@163.com
Yunan Cui
Dept. of Mathematics, Harbin University of Science and Technology, Harbin 150080, P. R. China
cuiya@hrbust.edu.cn
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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