Strong and Δ-convergence for mixed type total asymptotically nonexpansive mappings in CAT(0) spaces

Shih Sen Chang, Lin Wang, Heung Wing Joseph Lee, Chi Kin Chan

Research output: Journal article publicationJournal articleAcademic researchpeer-review

14 Citations (Scopus)

Abstract

It is our purpose in this paper first to introduce the class of total asymptotically nonexpansive nonself mappings and to prove the demiclosed principle for such mappings in CAT(0) spaces. Then, a new mixed Agarwal-O'Regan-Sahu type iterative scheme for approximating a common fixed point of two total asymptotically nonexpansive mappings and two total asymptotically nonexpansive nonself mappings is constructed. Under suitable conditions, some strong convergence theorems and Δ-convergence theorems are proved in a CAT(0) space. Our results improve and extend the corresponding results of Agarwal, O'Regan and Sahu (J. Nonlinear Convex Anal. 8(1):61-79, 2007), Guo et al. (Fixed Point Theory Appl. 2012:224, 2012. doi:10.1186/1687- 1812-2012-224), Sahin et al. (Fixed Point Theory Appl. 2013:12, 2013. doi:10.1186/1687-1812-2013-12), Chang et al. (Appl. Math. Comput. 219:2611-2617, 2012), Khan and Abbas (Comput. Math. Appl. 61:109-116, 2011), Khan et al. (Nonlinear Anal. 74:783-791, 2011), Xu (Nonlinear Anal., Theory Methods Appl. 16(12):1139-1146, 1991), Chidume et al. (J. Math. Anal. Appl. 280:364-374, 2003) and others.
Original languageEnglish
Article number122
JournalFixed Point Theory and Applications
Volume2013
DOIs
Publication statusPublished - 1 Jan 2013

Keywords

  • CAT(0) space
  • Demiclosed principle
  • Mixed Agarwal-O'Regan-Sahu type iterative scheme
  • Strong convergence
  • Total asymptotically nonexpansive mappings
  • Total asymptotically nonexpansive nonself mappings
  • Δ-convergence

ASJC Scopus subject areas

  • Geometry and Topology
  • Applied Mathematics

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