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arXiv · 2010.05554

On a theorem about Mosco convergence in Hadamard spaces

Arian Berdellima
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Abstract

Let $(f^n),f$ be a sequence of proper closed convex functions defined on a Hadamard space. We show that the convergence of proximal mappings $J^n_{\lambda}x$ to $J_{\lambda}x$, under certain additional conditions, imply Mosco convergence of $f^n$ to $f$. This result is a converse to a theorem of Bacak about Mosco convergence in Hadamard spaces.

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Arian Berdellima. 2020-10-12. On a theorem about Mosco convergence in Hadamard spaces. https://doi.org/10.4153/s000843952200008x

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