Geodesic
Stability of positive part of unit ball in Orlicz spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 46 (2005) no. 3, pp. 413-424.

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The aim of this paper is to investigate the stability of the positive part of the unit ball in Orlicz spaces, endowed with the Luxemburg norm. The convex set $Q$ in a topological vector space is stable if the midpoint map $\Phi\colon Q\times Q\rightarrow Q$, $\Phi(x,y) =(x+y)/2$ is open with respect to the inherited topology in $Q$. The main theorem is established: In the Orlicz space $L^\varphi(\mu)$ the stability of the positive part of the unit ball is equivalent to the stability of the unit ball.
Classification : 46Axx, 46B20, 46Cxx, 46E30, 52A41
Keywords: stable convex set 
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     title = {Stability of positive part of unit ball in {Orlicz} spaces},
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Grząślewicz, Ryszard; Seredyński, Witold. Stability of positive part of unit ball in Orlicz spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 46 (2005) no. 3, pp. 413-424. http://geodesic.mathdoc.fr/item/CMUC_2005__46_3_a4/