Proximal Point Algorithms for a Hybrid Pair of Nonexpansive Single-Valued and Multi-Valued Mappings in Geodesic Metric Spaces
© 2017, Springer International Publishing. In this paper, we propose a new proximal point algorithm for finding a common element of the set of fixed points of nonexpansive single-valued mappings, the set of fixed points of nonexpansive multi-valued mappings, and the set of minimizers of convex and l...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Journal |
| Published: |
2018
|
| Subjects: | |
| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85014474299&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/57518 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Chiang Mai University |
| Summary: | © 2017, Springer International Publishing. In this paper, we propose a new proximal point algorithm for finding a common element of the set of fixed points of nonexpansive single-valued mappings, the set of fixed points of nonexpansive multi-valued mappings, and the set of minimizers of convex and lower semi-continuous functions. We obtain Δ -convergence and strong convergence of the proposed algorithm to a common element of the three sets in CAT(0) spaces. Furthermore, we apply our convergence results to obtain in a special space of CAT(0) spaces, so-called R-tree, under the gate condition. A numerical example to support our main results is also given. |
|---|