Description

• Title:
  On Halpern-type sequences with applications in Hadamard spaces
• Creator:
  Rachpira, Nattapol;
  Saejung, Satit;
  Yotkaew, Pongsakorn
• Description:
  We introduce the concept of quasi-Halpern sequence which generalizes the concept of Halpern sequences introduced by Jaipranop and Saejung \cite{JS-2020} from Hilbert spaces to Hadamard spaces. Our notion also allows some error computation in the sequence. Furthermore, we establish a necessary and sufficient condition for the strong convergence of a quasi-Halpern sequence. Additionally, we have derived two strong convergence theorems for approximating fixed points of nonexpansive sequences or strongly quasi-nonexpansive sequences. Moreover, we apply our results to the problem of finding a zero of a certain monotone operator and a minimizer of a convex function in a Hadamard space. Our result generalizes and improves the recent results of Kohsaka and Kimura \cite{KK-2016} and of Okeke \cite{O-2023}.
• Object availability:
  free access
• Date:
  2025.06.14
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Online First Articles; 1 - 24;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/62298/42797 ;https://apcz.umk.pl/TMNA/article/view/62298/42798
• Subject:
  Fixed point;
  Hadamard space;
  Halpern sequence;
  resolvent operator;
  strong convergence;
  47H09, 47H05, 47J25
• Identifier: https://apcz.umk.pl/TMNA/article/view/62298
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other