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An algorithm for finding a common solution for a system of mixed equilibrium problem, quasi-variational inclusion problem and fixed point problem of nonexpansive semigroup

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Języki publikacji
EN
Abstrakty
EN
In this paper, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed points for a nonexpansive semigroup and the set of solutions of the quasi-variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in a Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in the literature.
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465--484
Opis fizyczny
Bibliogr. 13 poz.
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autor
autor
  • Yibin University Department of Mathematics Yibin, Sichuan 644007, China, changss@yahoo.cn
Bibliografia
  • [1] L.C. Ceng, J.C. Yao, A hybrid iterative scheme for mixed equilibrium problems and fixed point problems, J. Comput. Appl. Math. 214 (2008), 186–201.
  • [2] S. Chang, Set-valued variational inclusions in Banach space, J. Math. Anal. Appl. 248 (2000), 438–454.
  • [3] S. Chang, Existence and approximation of solutions of Set-valued variational inclusions in Banach space, Nonlinear Anal. 47 (2001) 1, 583–594.
  • [4] S. Chang, H.W. Joseph Lee, C. Chan, A new method for solving equilibrium problem fixed point problem and variational inequality problem with application to optimization, Nonlinear Anal. 70 (2009), 3307–3319.
  • [5] V.F. Demyanov, G.E. Stavroulakis, L.N. Polyakova, P.D. Panagiotopoulos, Quasi-differentiability and Nonsmooth Modeling in Mechanics. Engineering and Economics, Kluwer Academic, Dordrecht, 1996.
  • [6] S. Li, L. Li, Y. Su, General iterative methods for a one-parameter nonexpansive semigroup in Hilbert space, Nonlinear Anal., Theory Methods Appl. 70, No. 9 (A), 2065–2071 (2009), doi:10.1016/j.na.2008.04.007.
  • [7] J.L. Lions, G. Stampacchia, Variational inequalities, Comm. Pure. Appl. Math. 20 (1967), 493–517.
  • [8] D. Pascali, Nolinear Mappings of Monotone Type, Sijthoff and Noordhoff International Publishers, The Netherlands, 1978.
  • [9] S. Saeidi, Iterative algorithms for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of families and semigroups of nonexpansive mappings, Nonlinear Anal. (2008), doi:10.1016/j.na.2008.09.009.
  • [10] T. Shimizu, W. Takahashi, Strong convergence to common fixed points of families of nonexpansive mappings, J. Math. Anal. Appl. 211 (1997), 71–83.
  • [11] S. Takahashi, W. Takahshi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert space, J. Math. Anal. Appl. 331 (2007), 506–515.
  • [12] H.K. Xu, An iterative approach to quadratic optimization, J. Optim. Theory Appl. 116 (2003) 3, 659–678.
  • [13] S. Zhang, J.H. Joseph Lee, C.K. Chan, Algorithms of common solutions for quasi-variational inclusion and fixed point problems, Appl. Math. Mech. 29 (2008), 1–11.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGHT-0003-0019
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