Abstract and Applied Analysis

A Modified Mixed Ishikawa Iteration for Common Fixed Points of Two Asymptotically Quasi Pseudocontractive Type Non-Self-Mappings

Yuanheng Wang and Huimin Shi

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

A new modified mixed Ishikawa iterative sequence with error for common fixed points of two asymptotically quasi pseudocontractive type non-self-mappings is introduced. By the flexible use of the iterative scheme and a new lemma, some strong convergence theorems are proved under suitable conditions. The results in this paper improve and generalize some existing results.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 129069, 7 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412278801

Digital Object Identifier
doi:10.1155/2014/129069

Mathematical Reviews number (MathSciNet)
MR3191017

Zentralblatt MATH identifier
07021765

Citation

Wang, Yuanheng; Shi, Huimin. A Modified Mixed Ishikawa Iteration for Common Fixed Points of Two Asymptotically Quasi Pseudocontractive Type Non-Self-Mappings. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 129069, 7 pages. doi:10.1155/2014/129069. https://projecteuclid.org/euclid.aaa/1412278801


Export citation

References

  • K. Goebel and W. A. Kirk, “A fixed point theorem for asymptotically nonexpansive mappings,” Proceedings of the American Mathematical Society, vol. 35, pp. 171–174, 1972.
  • J. Schu, “Approximation of fixed points of asymptotically nonexpansive mappings,” Proceedings of the American Mathematical Society, vol. 112, pp. 143–151, 1991.
  • W. Takahashi, N.-C. Wong, and J.-C. Yao, “Attractive point and weak convergence theorems for new generalized hybrid mappings in Hilbert spaces,” Journal of Nonlinear and Convex Analysis, vol. 13, pp. 745–757, 2012.
  • Y. Kurokawa and W. Takahashi, “Weak and strong convergence theorems for nonspreading mappings in Hilbert spaces,” Nonlinear Analysis, Theory, Methods and Applications, vol. 73, no. 6, pp. 1562–1568, 2010.
  • H. K. Xu, “Vistosity approximation methods for nonexpansive mappings,” Journal of Mathematical Analysis and Applications, vol. 298, pp. 279–291, 2004.
  • D. R. Sahu, H.-K. Xu, and J.-C. Yao, “Asymptotically strict pseudocontractive mappings in the intermediate sense,” Nonlinear Analysis, Theory, Methods and Applications, vol. 70, no. 10, pp. 3502–3511, 2009.
  • J. K. Kim, D. R. Sahu, and Y. M. Nam, “Convergence theorem for fixed points of nearly uniformly L-Lipschitzian asymptotically generalized $\Phi $-hemicontractive mappings,” Nonlinear Analysis, Theory, Methods and Applications, vol. 71, no. 12, pp. e2833–e2838, 2009.
  • S. S. Chang, “Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings,” Proceedings of the American Mathematical Society, vol. 129, no. 3, pp. 845–853, 2001.
  • P. Cholamjiak and S. Suantai, “A new hybrid algorithm for variational inclusions, generalized equilibrium problems, and a finite family of quasi-nonexpansive mappings,” Fixed Point Theory and Applications, vol. 2009, Article ID 350979, 7 pages, 2009.
  • C. Klin-Eam and S. Suantai, “Strong convergence of composite iterative schemes for a countable family of nonexpansive mappings in Banach spaces,” Nonlinear Analysis, Theory, Methods and Applications, vol. 73, no. 2, pp. 431–439, 2010.
  • S. Plubtieng and K. Ungchittrakool, “Approximation of common fixed points for a countable family of relatively nonexpansive mappings in a Banach space and applications,” Nonlinear Analysis, Theory, Methods and Applications, vol. 72, no. 6, pp. 2896–2908, 2009.
  • T. Suzuki, “Strong convergence theorems for infinite families of nonexpansive mappings in general Banach spaces,” Fixed Point Theory and Applications, vol. 2005, no. 1, pp. 103–123, 2005.
  • L.-C. Zeng and J.-C. Yao, “Implicit iteration scheme with perturbed mapping for common fixed points of a finite family of nonexpansive mappings,” Nonlinear Analysis, Theory, Methods and Applications, vol. 64, no. 11, pp. 2507–2515, 2006.
  • G. Marino and H.-K. Xu, “A general iterative method for nonexpansive mappings in Hilbert spaces,” Journal of Mathematical Analysis and Applications, vol. 318, no. 1, pp. 43–52, 2006.
  • Y.-H. Wang and Y.-H. Xia, “Strong convergence for asymptotically pseudocontractions with the demiclosedness principle in Banach spaces,” Fixed Point Theory and Applications, vol. 2012, 8 pages, 2012.
  • Y.-H. Wang and W. F. Xuan, “Convergence theorems for common fixed points of a finite family of relatively nonexpansive mappings in Banach spaces,” Abstract and Applied Analysis, vol. 2013, Article ID 259470, 7 pages, 2013.
  • L.-C. Zeng and J.-C. Yao, “Stability of iterative procedures with errors for approximating common fixed points of a couple of q-contractive-like mappings in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 321, no. 2, pp. 661–674, 2006.
  • L.-C. Zeng, T. Tanaka, and J.-C. Yao, “Iterative construction of fixed points of nonself-mappings in Banach spaces,” Journal of Computational and Applied Mathematics, vol. 206, no. 2, pp. 814–825, 2007.
  • L. C. Zeng, N. C. Wong, and J. C. Yao, “Convergence analysis of iterative sequences for a pair of mappings in Banach spaces,” Acta Mathematica Sinica, vol. 24, no. 3, pp. 463–470, 2008.
  • X. Wu, J. C. Yao, and L. C. Zeng, “Uniformly normal structure and strong convergence theorems for asymptotically pseudocontractive mappings,” Journal of Nonlinear and Convex Analysis, vol. 6, no. 3, pp. 453–463, 2005.
  • L.-C. Ceng, N.-C. Wong, and J.-C. Yao, “Fixed point solutions of variational inequalities for a finite family of asymptotically nonexpansive mappings without common fixed point assumption,” Computers and Mathematics with Applications, vol. 56, no. 9, pp. 2312–2322, 2008.
  • C. E. Chidume, E. U. Ofoedu, and H. Zegeye, “Strong and weak convergence theorems for asymptotically nonexpansive mappings,” Journal of Mathematical Analysis and Applications, vol. 280, no. 2, pp. 364–374, 2003.
  • H. Zegeye, M. Robdera, and B. Choudhary, “Convergence theorems for asymptotically pseudocontractive mappings in the intermediate sense,” Computers and Mathematics with Applications, vol. 62, no. 1, pp. 326–332, 2011.
  • S.-S. Chang, “Some problems and results in the study of nonlinear analysis,” Nonlinear Analysis, Theory, Methods and Applications, vol. 30, no. 7, pp. 4197–4208, 1997. \endinput