Kyungpook Mathematical Journal

  • 제48권1호
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  • Pages.133-142
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  • 2008
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Strong Convergence Theorems for Asymptotically Nonexpansive Mappings by Hybrid Methods

  • Qin, Xiaolong (Department of Mathematics, Tianjin Polytechnic University) ;
  • Su, Yongfu (Department of Mathematics, Tianjin Polytechnic University) ;
  • Shang, Meijuan (Department of Mathematics, Tianjin Polytechnic University, Department of Mathematics, Shijiazhuang University)
  • 투고 : 2007.01.08
  • 발행 : 2008.03.31
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초록

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.

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참고문헌

  1. C. E. Chidume and S. A. Mutangadura, An example on the Mann iteration method for Lipschitz pseudocontractions, Proc. Am. Math. Soc., 129(2001), 2359-2363. https://doi.org/10.1090/S0002-9939-01-06009-9
  2. K. Goebel and W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Am. Math. Soc., 35(1972), 171-174. https://doi.org/10.1090/S0002-9939-1972-0298500-3
  3. A. Genel and J. Lindenstrass, An example concerning fixed points, Israel J. Math., 22(1975), 81-86. https://doi.org/10.1007/BF02757276
  4. B. Halpern, Fixed points of nonexpanding maps, Bull. Am. Math. Soc., 73(1967), 957-961. https://doi.org/10.1090/S0002-9904-1967-11864-0
  5. S. Ishikawa, Fixed points by a new iteration medthod, Proc. Am. Math. Soc., 44(1974), 147-150. https://doi.org/10.1090/S0002-9939-1974-0336469-5
  6. T. H. Kim and H. K. Xu, Strong convergence of modified mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal., 64(2006), 1140-1152. https://doi.org/10.1016/j.na.2005.05.059
  7. P. K. Lin, K. K. Tan and H. K. Xu, Demiclosedness principle and asymptotically nonexpansive mappings, Nonlinear Anal., 24(1995), 929-946. https://doi.org/10.1016/0362-546X(94)00128-5
  8. W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc., 4(1953), 506-510. https://doi.org/10.1090/S0002-9939-1953-0054846-3
  9. C. Martinez-Yanes and H. K Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal., 64(2006), 2400-2411. https://doi.org/10.1016/j.na.2005.08.018
  10. K. Nakajo and W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl., 279(2003), 372-379. https://doi.org/10.1016/S0022-247X(02)00458-4
  11. S. Reich, Weak convergence theorems for nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., 67(1979), 274-276. https://doi.org/10.1016/0022-247X(79)90024-6

피인용 문헌

  1. Hybrid Mann–Halpern Iteration Methods for Finding Fixed Points Involving Asymptotically Nonexpansive Mappings and Semigroups vol.42, pp.2, 2014, https://doi.org/10.1007/s10013-014-0071-5
  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