대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제27권3호
  • /
  • Pages.505-512
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  • 2012
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  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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WEAK CONVERGENCE THEOREMS FOR EQUILIBRIUM PROBLEMS AND NONEXPANSIVE MAPPINGS AND NONSPREADING MAPPINGS IN HILBERT SPACES

  • Jiang, Li (Department of Mathematics Tianjin Polytechnic University) ;
  • Su, Yongfu (Department of Mathematics Tianjin Polytechnic University)
  • 투고 : 2011.01.07
  • 발행 : 2012.07.31
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초록

In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mappings and nonspreading mappings and the set of solution of an equilibrium problem on the setting of real Hilbert spaces.

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참고문헌

  1. 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
  2. Y. Kurokawa andW. Takahashi, Weak and strong convergence theorems for nonspreading mappings in Hilbert space, Nonlinear Anal. 73 (2010), no. 6, 1562-1568. https://doi.org/10.1016/j.na.2010.04.060
  3. S. Matsushita and W. Takahashi, A strong convergence theorem for relatively nonexpan- sive mappings in a Banach space, J. Approx. Theory 134 (2005), no. 2, 257-266. https://doi.org/10.1016/j.jat.2005.02.007
  4. K. Nakajo and W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003), no. 2, 372-378. https://doi.org/10.1016/S0022-247X(02)00458-4
  5. A. Tada and W. Takahashi, Strong convergence theorem for an equilibrium problem and a nonexpansive mapping, Nonlinear analysis and convex analysis, 609-617, Yokohama Publ., Yokohama, 2007.
  6. A. Tada and W. Takahashi, Weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem, J. Optim. Theory Appl. 133 (2007), no. 3, 359-370. https://doi.org/10.1007/s10957-007-9187-z
  7. W. Takahashi, Fixed point theorems for new nonlinear mappings in a Hilbert space, J. Nonlinear Convex Anal. 11 (2010), no. 1, 79-88.