Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Midpoint locally uniform rotundity
  • Musielak-Orlicz-Bochner function spaces
  • Luxemburg norm

Mathematics Subject Classification

46E30, 46B20

Suggested citation

S. Shang, Y. Cui, Y. Fu. “Midpoint Locally Uniform Rotundity of Musielak-Orlicz-Bochner Function Spaces Endowed with the Luxemburg Norm.” Journal of Convex Analysis 19 (2012), No. 1, 213–223.

Copyright Heldermann Verlag 2012