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
Dept. of Mathematics, Northeast Forestry University, Harbin 150040, P. R. China
Dept. of Mathematics, Harbin University of Science and Technology, Harbin 150080, P. R. China
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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