Journals / Hacettepe Journal of Mathematics and Statistics / 2012 / Volume: 41 Issue: 6

APPROXIMATION OF FIXED POINTS OF ASYMPTOTICALLY κ-STRICT PSEUDOCONTRACTIONS IN A BANACH SPACE

Pages
—
Publication Date
2012-06-01
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

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

In this paper, weak convergence theorems of a finite family of asymptotically k-strict pseudo-contractions are established in the framework of 2-uniformly smooth and uniformly convex Banach spaces.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, weak convergence theorems of a finite family of asymptotically k-strict pseudo-contractions are established in the framework of 2-uniformly smooth and uniformly convex Banach spaces.
📊
Key Findings & Data:In this paper, weak convergence theorems of a finite family of asymptotically k-strict pseudo-contractions are established in the framework of 2-uniformly smooth and uniformly convex Banach spaces.
💡
Conclusion & Impact:In this paper, weak convergence theorems of a finite family of asymptotically k-strict pseudo-contractions are established in the framework of 2-uniformly smooth and uniformly convex Banach spaces.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Asymptotically k-strict pseudo-contraction · Fixed point · Non-expansive mapping

Abstract

In this paper, weak convergence theorems of a finite family of asymptotically k-strict pseudo-contractions are established in the framework of 2-uniformly smooth and uniformly convex Banach spaces.

🔖

Cite This Article

Wu, C. (2012). APPROXIMATION OF FIXED POINTS OF ASYMPTOTICALLY κ-STRICT PSEUDOCONTRACTIONS IN A BANACH SPACE. Hacettepe Journal of Mathematics and Statistics, Volume: 41 Issue: 6. https://ajindex.com/articles/1403505

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (12)

  1. Acedo, G. L. and Xu, H. K. Iterative methods for strict pseudo-contractions in Hilbert spaces, Nonlinear Anal. 67, 2258–2271, 2007.
  2. Browder, F. E. and Petryshyn, W. V. Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl. 20, 197–228, 1967.
  3. Goebel, K. and Kirk, W. A. A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35, 171–174, 1972.
  4. Kr¨uppel, M. On an inequality for nonexpansive mappings in uniformly convex Banach spaces, Rostock. Math. Kolloq. 51, 25–32, 1997.
  5. Mann, W.R. Mean value methods in iteration, Proc. Amer. Math. Soc. 4, 506–510, 1953.
  6. Marino, G. and Xu, H. K. Weak and strong convergence theorems for strict pseudo- contractions in Hilbert space, J. Math. Anal. Appl. 329, 336–346, 2007.
  7. Osilike, M. O. and Shehu, Y. Explicit averaging cyclic algorithm for common fixed points of asymptotically strictly pseudocontractive maps, Appl. Math. Comput. 213, 548–553, 2009. [8] Osilike, M. O. and Shehu, Y. Explicit averaging cyclic algorithm for common fixed points of a finite family of asymptotically strictly pseudocontractive maps in Banach spaces, Comput. Math. Appl. 57, 1502–1510, 2009.
  8. Qin, X., Cho, Y. J., Kang, S. M. and Shang, M. A hybrid iterative scheme for asymptotically image-strict pseudo-contractions in Hilbert spaces, Nonlinear Anal. 70, 1902–1911, 2009.
  9. Qin, X. Approximation of a zero point of accretive operator in Banach spaces, J. Math. Anal. Appl. 329, 415–424, 2007. [11] Qihou, L. Convergence theorems of the sequence of iterates for asymptotically demicontrac- tive and hemicontractive mappings, Nonlinear Anal. 26, 1835–1842, 1996.
  10. Reich, S. Weak convergence theorems for nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 67, 274–276, 1979.
  11. Tan, K. K. and Xu, H. K. Approximating fixed points of nonexpansive mappings by the Ishikawaiteration process, J. Math. Anal. Appl. 178, 301–308, 1993.
  12. Xu, H. K. Inequalities in Banach spaces with applications, Nonlinear Anal. 16, 1127–1138, 1991.