Journal of Convex Analysis 19 (2012), No. 1, 213--223
Copyright Heldermann Verlag 2012
Midpoint Locally Uniform Rotundity of Musielak-Orlicz-Bochner Function Spaces Endowed with the Luxemburg Norm
Shaoqiang Shang
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P. R. China
sqshang@163.com
Yunan Cui
Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, P. R. China
cuiya@hrbust.edu.cn
Yongqiang Fu
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P. R. China
Criteria for midpoint locally uniform rotundity of Musielak-Orlicz-Bochner function spaces equipped with the Luxemburg norm are given. We also prove that, in Musielak-Orlicz-Bochner function spaces generated by midpoint locally uniformly rotund Banach space, midpoint locally uniform rotundity and rotundity are equivalent.
Keywords: Midpoint locally uniform rotundity, Musielak-Orlicz-Bochner function spaces, Luxemburg norm.
MSC: 46E30, 46B20
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