# Proximal point algorithm involving fixed point of nonexpansive mapping in 𝑝-uniformly convex metric space

Proximal point algorithm involving fixed point of nonexpansive mapping in 𝑝-uniformly convex... AbstractWe prove some important properties of the p-resolvent mapping recently introduced byB. J. Choi and U. C. Ji,The proximal point algorithm in uniformly convex metric spaces,Commun. Korean Math. Soc. 31 2016, 4, 845–855,in p-uniformly convex metric space. Furthermore, we introduce a modified Mann-type PPA involving nonexpansive mapping and prove that the sequence generated by the algorithm converges to a common solution of a finite family of minimization problems, which is also a fixed point of a nonexpansive mapping in the framework of a complete p-uniformly convex metric space. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Pure and Applied Mathematics de Gruyter

# Proximal point algorithm involving fixed point of nonexpansive mapping in 𝑝-uniformly convex metric space

, Volume 10 (4): 10 – Oct 1, 2019
10 pages

/lp/de-gruyter/proximal-point-algorithm-involving-fixed-point-of-nonexpansive-mapping-bBNNS2uAGU
Publisher
de Gruyter
© 2019 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1869-6090
eISSN
1869-6090
DOI
10.1515/apam-2018-0026
Publisher site
See Article on Publisher Site

### Abstract

AbstractWe prove some important properties of the p-resolvent mapping recently introduced byB. J. Choi and U. C. Ji,The proximal point algorithm in uniformly convex metric spaces,Commun. Korean Math. Soc. 31 2016, 4, 845–855,in p-uniformly convex metric space. Furthermore, we introduce a modified Mann-type PPA involving nonexpansive mapping and prove that the sequence generated by the algorithm converges to a common solution of a finite family of minimization problems, which is also a fixed point of a nonexpansive mapping in the framework of a complete p-uniformly convex metric space.

### Journal

Advances in Pure and Applied Mathematicsde Gruyter

Published: Oct 1, 2019