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

Authors
  • Ugwunnadi, Godwin C.
  • Izuchukwu, Chinedu
  • Mewomo, Oluwatosin T.
Type
Published Article
Journal
Advances in Pure and Applied Mathematics
Publisher
De Gruyter
Publication Date
Dec 05, 2018
Volume
10
Issue
4
Pages
437–446
Identifiers
DOI: 10.1515/apam-2018-0026
Source
De Gruyter
Keywords
License
Yellow

Abstract

We prove some important properties of the p-resolvent mapping recently introduced by B. 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.

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