
Journal of Convex Analysis 22 (2015), No. 3, 747768 Copyright Heldermann Verlag 2015 Uniform Rotundity and kUniform Rotundity in MusielakOrliczBochner 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 MusielakOrliczBochner function spaces equipped with Orlicz norm are given. We also prove that, in MusielakOrliczBochner function spaces, uniform rotundity and $k$uniform rotundity are equivalent. Moreover, we give a sufficient condition for a MusielakOrliczBochner function space to have the fixed point property. Keywords: MusielakOrliczBochner function spaces, uniform rotundity, kuniform rotundity, Orlicz norm, fixed point. MSC: 46E30, 46B20 [ Fulltextpdf (174 KB)] for subscribers only. 