Journal of Convex Analysis 34 (2027), No. 1, 161--181
Copyright Heldermann Verlag 2027
On the Uniform Convexity of the Squared Distance
Andrei Sipos
Research Center for Logic, Optimization and Security, Dept. of Computer Science, Faculty of Mathematics and Computer Science, University of Bucharest, Romania
andrei.sipos@fmi.unibuc.ro
In 1983, Zalinescu showed that the squared norm of a uniformly convex normed space is uniformly convex on bounded subsets. We extend this result to the metric setting of uniformly convex hyperbolic spaces. We derive applications to the convergence of shadow sequences and to proximal minimization.
Keywords: Uniform convexity, hyperbolic spaces, uniformly convex functions, shadow sequences, proximal maps.
MSC: 51F99, 52A55, 53C23.
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