On the uniform convexity of the squared distance

2025/03/05 by Sipos, Andrei
#51F99 #52A55 #53C23 #FOS: Mathematics #Metric Geometry (math.MG) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2503.03442

Abstract

In 1983, Zălinescu 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.

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• Convexity of sets and quadratic functions on the hyperbolic space
• On Klee's problem of convex bodies in Banach spaces
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