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Nonlinear algorithms for a common solution of a system of variational inequalities, a split equilibrium problem and fixed point problems

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강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2016.09|한국수학논문집 (Korean Journal of Mathematics)|제24권 제3호|pp. 495-524|DOI http://dx.doi.org/10.11568/kjm.2016.24.3.495

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키워드

fixed pointNonexpansive mappingvariational inequality.mixed equilibrium problem
주제분류수학

초록

In this paper, we propose an iterative algorithm for finding a common solution of a system of generalized equilibrium problems, a split equilibrium problem and a hierarchical fixed point problem over the common fixed points set of a finite family of nonexpansive mappings in Hilbert spaces. Furthermore, we prove that the proposed iterative method has strong convergence under some mild conditions imposed on algorithm parameters. The results presented in this paper improve and extend the corresponding results reported by some authors recently.

Abstract

In this paper, we propose an iterative algorithm for finding a common solution of a system of generalized equilibrium problems, a split equilibrium problem and a hierarchical fixed point problem over the common fixed points set of a finite family of nonexpansive mappings in Hilbert spaces. Furthermore, we prove that the proposed iterative method has strong convergence under some mild conditions imposed on algorithm parameters. The results presented in this paper improve and extend the corresponding results reported by some authors recently.

참고문헌 (28)

  1. Q. H. Ansari, "Generalized Convexity, Nonsmooth Variational Inequalities and Nonsmooth Optimization" (2014), CRC Press
  2. Q. H. Ansari, "The existence of nonlinear inequalities", Appl. Math Lett, 12, pp.89~92 (1999)
  3. E. Blum, "From optimization and variational inequalities to equi-librium problems", Math. Stud, 63, pp.123~145 (1994)
  4. A. Bnouhachem, "A self-adaptive method for solving general mixed variational inequalities", J. Math. Anal. Appl, 309, pp.136~150 (2005)
  5. A. Bnouhachem, "A new projection and contraction method for linear variational inequalities", J. Math. Anal. Appl, 314, pp.513~525 (2006)
  6. N. Buong, "An explicit iterative algorithm for a class of vari-ational inequalities in Hilbert spaces", J. Optim. Theory Appl, 151, pp.513~524 (2011)
  7. L. C. Ceng, "Iterative methods for gener-alized equilibrium problems, systems of general generalized equilibrium problems and fixed point problems for nonexpansive mappings in Hilbert spaces", Fixed Point Theory, 12, pp.293~308 (2011)
  8. L. C. Ceng, "Some iterative methods for finding xed points and for solving constrained convex minimiization problems", Nonlinear Anal, 74, pp.5286~5302 (2011)
  9. L. C. Ceng, "Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities", Math Methods Oper. Res, 67, pp.375~390 (2008)
  10. L. C. Ceng, "A relaxed extragradient-like method for a generalized mixed equilibrium problem, a general system of generalized equilibria and a fixed point problem", Nonlinear Anal, 72, pp.1922~1937 (2010)
  11. Y. Censor, "A multiprojection algorithm using Bregman projections in a product space", Numer. Algorithms, 8, pp.221~239 (1994)
  12. S. S. Chang, "A new method for solving equilibrium problem, fixed point problem and variational inequality problem with application to optimization", Nonlinear Anal, 70, pp.3307~3319 (2009)
  13. F. Cianciaruso, "A hybrid projection algorithm for finding solutions of mixed equilibrium problem and variational inequal-ity problem", Fixed Point Theory Appl, 2010 (2010)
  14. P. L. Combetters, "Equilibrium programming using proximal like algorithms", Math. Program, 78, pp.29~41 (1997)
  15. P. Duan, "Generalized viscosity approximation methods for nonexpan-sive mappings", Fixed Point Theory Appl, 2014, pp.68~ (2014)
  16. K. Goebel, "Topics in Metric Fixed Point Theory" (1990), Cambridge University Press
  17. G. Lopez, "Biomedical Mathematics Promising Directions: In Imaging Therapy Planning and Inverse Problems", pp.243~279 (2009)
  18. P. E. Mainge, "Strong convergence of an iterative method for hierarchical fixed point problems", Pac. J. Optim, 3, pp.529~538 (2007)
  19. X. Qin, "A general iterative method for equilibrium problem and fixed point in Hilbert spaces", Nonlinear Anal, 69, pp.3897~3909 (2008)
  20. T. Suzuki, "Strong convergence of Krasnoselskii and Mann's type sequences for one parameter nonexpansive semigroups without Bochner integrals", J. Math. Anal. Appl, 35, pp.227~239 (2005)
  21. N. Suzuki, "Moudafi's viscosity approximations with Meir-Keeler contractions", J. Math. Anal. Appl, 325, pp.342~352 (2007)
  22. M. Tian, "A general iterative algorithm for nonexpansive mappings in Hilbert spaces", Nonlinear Anal, 73, pp.689~694 (2010)
  23. R. U. Verma, "Projection methods, algorithms and a new system of nonlinear variational inequalities", Comput. Math. Appl, 41, pp.1025~1031 (2001)
  24. R. U. Verma, "General convergence analysis for two-step projection methods and applications to variational problems", Appl. Math. Lett, 18, pp.1286~1292 (2005)
  25. H. K. Xu, "An iterative approach to quadratic optimization", J. Optim. Theory and Appl, 116, pp.659~678 (2003)
  26. I. Yamada, "Inherently Parallel Algorithms in Fea-sibility and Optimization and Their Application", pp.473~504 (2001), North-Holland
  27. C. Zhang, "A new explicit iterative algorithm for solving a class of variational inequalities over the common fixed points set of a finite family of nonexpansive mappings", Fixed Point Theory Appl, 2014, pp.60~ (2014)
  28. H. Y. Zhou, "A simpler explicit iterative algorithm for a class of variational inequalities in Hilbert spaces", J. Optim. Theory Appl, 161, pp.716~727 (2014)

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