Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2016; 31(4): 845-855

Online first article September 30, 2016      Printed October 31, 2016

https://doi.org/10.4134/CKMS.c150114

Copyright © The Korean Mathematical Society.

The proximal point algorithm in uniformly convex metric spaces

Byoung Jin Choi and Un Cig Ji

Sungkyunkwan University, Chungbuk National University

Abstract

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We introduce the proximal point algorithm in a $p$-uniformly convex metric space. We first introduce the notion of $p$-resolvent map in a $p$-uniformly convex metric space as a generalization of the Moreau-Yosida resolvent in a CAT($0$)-space, and then we secondly prove the convergence of the proximal point algorithm by the $p$-resolvent map in a $p$-uniformly convex metric space.

Keywords: $p$-uniformly convex metric space, $p$-resolvent map, proximal point algorithm

MSC numbers: Primary 51F99, 47J25

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