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Resolvents of convex functions in complete geodesic metric spaces with negative curvature

  • Takuto KajimuraEmail author
  • Yasunori Kimura
Article

Abstract

In this paper, we define a resolvent of a proper lower semicontinuous convex function in a complete geodesic space with negative curvature and we show its well-definedness and fundamental properties. We further show a fixed point theorem for hyperbolically nonspreading mappings, which can be applied to the resolvent defined in this paper. We also apply these results to convex optimization problems in complete geodesic spaces with negative curvature.

Keywords

Resolvent approximation fixed point geodesic space nonspreading 

Mathematics Subject Classification

47H10 52A41 

Notes

Acknowledgements

This work was supported by JSPS KAKENHI Grant Number 15K05007.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Information ScienceToho UniversityFunabashiJapan

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