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Journals / Hacettepe Journal of Mathematics and Statistics / 2011 / Cilt: 40 - Sayı: 4

Some $Delta$-convergence theorems in CAT(0) spaces

Mujahid ABBAS
Safeer Hussain KHAN
Pages
563–569
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

This process is independent of and simpler than the Ishikawa type iteration process.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we use an iteration process for approximating common fixed points of two nonexpansive mappings by △- and strong conver- gence in CAT(0) spaces.
📊
Key Findings & Data:In this paper, we use an iteration process for approximating common fixed points of two nonexpansive mappings by △- and strong conver- gence in CAT(0) spaces.
💡
Conclusion & Impact:This process is independent of and simpler than the Ishikawa type iteration process.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, we use an iteration process for approximating common fixed points of two nonexpansive mappings by △- and strong conver- gence in CAT(0) spaces. This process is independent of and simpler than the Ishikawa type iteration process.

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Cite This Article

ABBAS, M., KHAN, S. H. (2022). Some $Delta$-convergence theorems in CAT(0) spaces. Hacettepe Journal of Mathematics and Statistics, Cilt: 40 - Sayı: 4, 563–569. https://ajindex.com/articles/530585

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References (17)

  1. Bridson, M. and Haefliger, A. Metric Spaces of Non-Positive Curvature (Springer-Verlag, Berlin, Heidelberg, 1999)
  2. Bruhat, F. and Tits, J. Groupes reductifs sur un corps local. I. Donnees radicielles valuees, Inst. Hautes ´Etudes Sci. Publ. Math. 41, 5–251, 1972
  3. Burago, D., Burago, Y. and Ivanov, S. A Course in Metric Geometry, in: Graduate Studies in Math. 33, Amer. Math. Soc., Providence, RI, 2001
  4. Das, G. and Debata, J. P. Fixed points of quasi-nonexpansive mappings, Indian J. Pure. Appl. Math. 17, 1263–1269, 1986
  5. Dhompongsa, S., Kirk,W.A. and Panyanak, B. Nonexpansive set-valued mappings in metric and Banach spaces, J. Nonlinear Convex Anal. 8, 35–45, 2007
  6. Dhompongsa, S., Kirk, W.A. and Sims, B. Fixed points of uniformly lipschitzian mappings, Nonlinear Anal. 65, 762–772, 2006
  7. Dhompongsa, S. and Panyanak, B. On △-convergence theorems in CAT(0) spaces, Comput. Math. Appl. 56, 2572–2579, 2008
  8. Fukhar-ud-din, H. and Khan, S.H. Convergence of iterates with errors of asymptotically quasi-nonexpansive mappings and applications, J. Math. Anal. Appl. 328, 821–829, 2007
  9. Goebel, K. and Reich, S. Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings (Marcel Dekker, Inc., New York, 1984)
  10. Gromov, M. Metric structure for Riemannian and non-Riemannian spaces, Progr. Math. 152, Birkhauser, Boston, 1984
  11. Kirk, W.A. and Panyanak, B. A concept of convergence in geodesic spaces, Nonlinear Anal. 68, 3689–3696, 2008
  12. Khan, S.H. and Fukhar-ud-din, H. Weak and strong convergence of a scheme with errors for two nonexpansive mappings, Nonlinear Anal. 8, 1295–1301, 2005
  13. Khan, S.H. and Takahashi, W. Approximating common fixed points of two asymptotically nonexpansive mappings, Sci. Math. Japan 53 (1), 143–148, 2001
  14. Lim, T.C. Remarks on some fixed point theorems, Proc. Amer. Math. Soc. 60, 179–182, 1976
  15. Reich, S. and Shafrir, I. Nonexpansive iterations in hyperbolic space, Nonlinear Anal. 15, 537–558, 1990
  16. Takahashi, W. Iterative methods for approximation of fixed points and their applications, J. Oper. Res. Soc. Japan. 43 (1), 87–108, 2000
  17. Takahashi, W. and Tamura, T. Limit theorems of operators by convex combinations of nonexpansive retractions in Banach spaces, J. Approx. Theory 91 (3), 386–397, 1997.