Abstract

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

Author information

Contact details are reproduced from the original publication and may be historical.

Andrei Sipoş

(1) Research Center for Logic, Optimization and Security (LOS), Dept. of Computer Science, Faculty of Mathematics and Computer Science, University of Bucharest, Romania
(2) Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania
(3) Institute for Logic and Data Science, Bucharest, Romania

andrei.sipos@fmi.unibuc.ro

Keywords

  • Uniform convexity
  • hyperbolic spaces
  • uniformly convex functions
  • shadow sequences
  • proximal maps

Mathematics Subject Classification

51F99, 52A55, 53C23

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Suggested citation

A. Sipoş. “On the Uniform Convexity of the Squared Distance.” Journal of Convex Analysis 34 (2027), No. 1, 120–135. https://doi.org/10.68381/jca34009

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