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

Shaoqiang Shang; Yunan Cui

Abstract

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.

Author information

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

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

Keywords

Musielak-Orlicz-Bochner function spaces
uniform rotundity
k-uniform rotundity
Orlicz norm
fixed point

Mathematics Subject Classification

46E30, 46B20

Suggested citation

S. Shang, Y. Cui. “Uniform Rotundity and k-Uniform Rotundity in Musielak-Orlicz-Bochner Function Spaces and Applications.” Journal of Convex Analysis 22 (2015), No. 3, 747–768.