East Asian mathematical journal

  • 제26권1호
  • /
  • Pages.25-38
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  • 2010
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  • 1226-6973(pISSN)
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  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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A HYBRID ITERATIVE METHOD OF SOLUTION FOR MIXED EQUILIBRIUM AND OPTIMIZATION PROBLEMS

  • Zhang, Lijuan (COLLEGE OF MATHEMATICS AND COMPUTER HEBEI UNIVERSITY) ;
  • Chen, Jun-Min (COLLEGE OF MATHEMATICS AND COMPUTER HEBEI UNIVERSITY)
  • 투고 : 2009.05.14
  • 심사 : 2010.01.04
  • 발행 : 2010.01.31
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초록

In this paper, we introduce a hybrid iterative method for finding a common element of the set of solutions of a mixed equilibrium problem, the set of common mixed points of finitely many nonexpansive mappings and the set of solutions of the variational inequality for an inverse strongly monotone mapping in a Hilbert space. We show that the iterative sequences converge strongly to a common element of the three sets. The results extended and improved the corresponding results of L.-C.Ceng and J.-C.Yao.

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과제정보

연구 과제 주관 기관 : National Natural Science Foundation of China, Natural Science Foundation of Hebei Province, Department of Education of Hebei Province

참고문헌

  1. F. E. Browder and W. V. Petryshyn, Construction of Fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl. (1967), no. 20, 197-228. https://doi.org/10.1016/0022-247X(67)90085-6
  2. H. Iiduka and W. Takahashi, Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings, Nonlinear Anal. (2005), no. 613, 341-350.
  3. H. K. Xu, An iterative approach to quadratic optimization, J. Optim. Theory Appl.(2003), no. 116, 659-678. https://doi.org/10.1023/A:1023073621589
  4. L. C. Ceng and J. C. Yao, A hybrid iterative scheme for mixed equilibrium problems and fixed points problems, J. Comput. Appl. Math. (2008), no. 214 (1), 186-201. https://doi.org/10.1016/j.cam.2007.02.022
  5. R. T. Rockafellar, On the maximality of sums of nonlinear monotone operators, Trans. Amer. Math. Soc. (1970), no. 149, 75-88. https://doi.org/10.1090/S0002-9947-1970-0282272-5
  6. T. Suziki, Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals, J. Math. Anal. Appl.(2005), no. 305, 227-239. https://doi.org/10.1016/j.jmaa.2004.11.017
  7. W. Takahashi and K. Shimoji, Convergence theorems for nonexpansive mappings and feasibility problems, Math. Comput. Model. (2000), no. 32, 1463-1471. https://doi.org/10.1016/S0895-7177(00)00218-1