DOI QR코드

DOI QR Code

Strong Convergence Theorems for Asymptotically Nonexpansive Mappings by Hybrid Methods

Qin, Xiaolong;Su, Yongfu;Shang, Meijuan

  • Received : 2007.01.08
  • Published : 2008.03.31

Abstract

In this paper, we prove two strong convergence theorems for asymptotically nonexpansive mappings in Hibert spaces by hybrid methods. Our results extend and improve the recent ones announced by Nakajo, Takahashi [K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372-379], Kim, Xu [T. H. Kim, H. K. Xu, Strong convergence of modified mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal. 64 (2006) 1140-1152], Martinez-Yanes, Xu [C. Martinez-Yanes, H. K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006) 2400-2411] and some others.

Keywords

Asymptotically nonexpansive mapping;Hilbert space;nonexpansive mapping;fixed point

References

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  2. On hybrid projection methods for asymptotically quasi--nonexpansive mappings vol.215, pp.11, 2010, https://doi.org/10.1016/j.amc.2009.11.031
  3. On the convergence of hybrid projection algorithms for asymptotically quasi-ϕ-nonexpansive mappings vol.61, pp.4, 2011, https://doi.org/10.1016/j.camwa.2010.12.033
  4. Bregman weak relatively nonexpansive mappings in Banach spaces vol.2013, pp.1, 2013, https://doi.org/10.1186/1687-1812-2013-141