Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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CONVERGENCE OF ISHIKAWA'METHOD FOR GENERALIZED HYBRID MAPPINGS

  • Yan, Fangfang (Department of Mathematics Tianjin Polytechnic University) ;
  • Su, Yongfu (Department of Mathematics Tianjin Polytechnic University) ;
  • Feng, Qinsheng (Department of Mathematics Tianjin Polytechnic University)
  • Received : 2012.03.20
  • Published : 2013.01.31
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Abstract

In this paper, we first talk about a more wide class of nonlinear mappings, Then, we deal with weak convergence theorems for generalized hybrid mappings in a Hilbert space.

Keywords

References

  1. K. Aoyama, S. Iemoto, F. Kohsaka, andW. Takahashi, Fixed point and ergodic theorems for ${\lambda}$-hybrid mappings in Hilbert spaces, J. Nonlinear Convex Anal. 11 (2010), no. 2, 335-343.
  2. E. Blum and W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. Student 63 (1994), no. 1-4, 123-145.
  3. F. E. Browder, Convergence theorems for sequences of nonlinear operators in Banach spaces, Math. Z. 100 (1967), 201-225. https://doi.org/10.1007/BF01109805
  4. P. L. Combettes and A. Hirstoaga, Equilibrium programming in Hilbert spaces, J. Nonlinear Convex Anal. 6 (2005), no. 1, 117-136.
  5. K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, Cambridge University Press, Cambridge, 1990.
  6. B. Halpern, Fixed points of nonexpanding maps, Bull. Amer. Math. Soc. 73 (1967), 957-961. https://doi.org/10.1090/S0002-9904-1967-11864-0
  7. M. Hojo, W. Takahashi, and I. Termwuttipong, Strong convergence theorems for 2-generalized hybrid mappings in Hilbert spaces, Nonlinear Anal. 75 (2012), no. 4, 2166- 2176. https://doi.org/10.1016/j.na.2011.10.017
  8. S. Iemoto and W. Takahashi, Approximating fixed points of nonexpansive mappings and nonspreading mappings in a Hilbert space, Nonlinear Anal. 71 (2009), no. 12, 2082-2089. https://doi.org/10.1016/j.na.2009.03.064
  9. S. Ishikawa, Fixed points by a new iteration, Proc. Amer. Math. Soc. 44 (1974), 147-150. https://doi.org/10.1090/S0002-9939-1974-0336469-5
  10. S. Itoh and W. Takahashi, The common fixed point theory of single-valued mappings and multi-valued mappings, Pacific J. Math. 79 (1978), no. 2, 493-508. https://doi.org/10.2140/pjm.1978.79.493
  11. F. Kohsaka and W. Takahashi, Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces, Arch. Math. 91 (2008), no. 2, 166-177. https://doi.org/10.1007/s00013-008-2545-8
  12. F. Kohsaka and W. Takahashi, Existence and approximation of fixed points of firmly nonexpansive-type mappings in Banach spaces, SIAM J. Optim. 19 (2008), no. 2, 824-835. https://doi.org/10.1137/070688717
  13. P. Kocourek, W. Takahashi, and J.-C. Yao, Fixed point theorems and weak convergence theorems for generalized hybrid mappings in Hilbert spaces, Taiwanese J. Math. 14 (2010), no. 6, 2497-2511. https://doi.org/10.11650/twjm/1500406086
  14. W. R. Mann, Mean value methods in iteration method, Proc. Amer. Math. Soc. 4 (1953), 506-510. https://doi.org/10.1090/S0002-9939-1953-0054846-3
  15. Z. Opial, Weak convergence of the sequence of successive approximations for non-expansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591-597.
  16. W. Takahashi, Nonlinear Functional Analysis, Yokohoma Publishers, Yokohama, 2000.
  17. W. Takahashi, Introduction to Nonlinear and Convex Analysis, Yokohama Publishers, Yokohama, 2005.
  18. W. Takahashi and M. Toyoda, Weak convergence theorems for nonexpansive mappings and monotone mappings, J. Optim. Theory Appl. 118 (2003), no. 2, 417-482. https://doi.org/10.1023/A:1025407607560
  19. W. Takahashi and J.-C. Yao, Fixed point theorems and ergodic theorems for nonlinear mappings in Hilbert spaces, Taiwanese J. Math. 15 (2011), no. 2, 457-472. https://doi.org/10.11650/twjm/1500406216

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