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Weak convergence theorems for 2-generalized hybrid mappings and equilibrium problems

Fridoun Moradlou|Sattar Alizadeh
대한수학회 (The Korean Mathematical Society)|2016.10|대한수학회논문집 (Communications of the KMS)|제31권 제4호|pp. 765-777

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키워드

fixed pointHilbert spaceequilibrium problemweak conver\-gence
주제분류수학

초록

In this paper, we propose a new modified Ishikawa iteration for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of $2$-generalized hybrid mappings in a Hilbert space. Our results generalize and improve some existing results in the literature. A numerical example is given to illustrate the usability of our results.

Abstract

In this paper, we propose a new modified Ishikawa iteration for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of $2$-generalized hybrid mappings in a Hilbert space. Our results generalize and improve some existing results in the literature. A numerical example is given to illustrate the usability of our results.

참고문헌 (29)

  1. R. P. Agarwal, "Fixed Point Theory for Lipschitzian-type Mappings with Applications" (2009), Springer
  2. S. Alizadeh, "Weak and strong convergence theorems for m-generalized hybrid mappings in Hilbert spaces", Topol. Methods Nonlinear Anal, 46(1), pp.315~328 (2015)
  3. S. Alizadeh, "A strong convergence theorem for equilibrium problems and generalized hybrid mappings", Mediterr. J. Math, 13(1), pp.379~390 (2016)
  4. E. Blum, "From optimization and variational inequalities to equilibrium problems", Math. Student, 63(1-4), pp.123~145 (1994)
  5. L. C. Ceng, "An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings", J. Comput. Appl. Math, 223(2), pp.967~974 (2009)
  6. L. C. Ceng, "A hybrid iterative scheme for mixed equilibrium problems and fixed point problems", J. Comput. Appl. Math, 214(1), pp.186~201 (2008)
  7. C. E. Chidume, "An example of the Mann iteration method for Lipschitz pseudocontractions", Proc. Amer. Math. Soc, 129(8), pp.2359~2363 (2001)
  8. P. L. Combettes, "Equilibrium programming in Hilbert spaces", J. Nonlinear Convex Anal, 6(1), pp.117~136 (2005)
  9. S. D. Flam, "Equilibrium programming using proximal-like algorithms", Math. Programming, 78(1), pp.29~41 (1997)
  10. A. Genel, "An example concerning fixed points", Israel J. Math, 22(1), pp.81~86 (1975)
  11. F. Giannessi, "Equilibrium Problems: Nonsmooth Opti-mization and Variational Inequality Models" (2001), Kluwer Academics Publishers
  12. M. Hojo, "Strong convergence theorem for 2-generalized hybrid mapping in Hilbert spaces", Nonlinear Anal, 75(4), pp.2166~2176 (2012)
  13. S. Ishikawa, "Fixed points by a new iteration method", Proc. Amer. Math. Soc, 40, pp.147~150 (1974)
  14. S. Itoh, "The common fixed point theory of singlevalued mappings and multivalued mappings", Pacific J. Math, 79(2), pp.493~508 (1978)
  15. C. Jaiboon, "A hybrid extragradient viscosity approximation method for solving equilibrium problems and fixed point problems of infinitely many nonexpansive mappings", Fixed Point Theory Appl, 2009, pp.32~ (2009)
  16. C. Jaiboon, "Weak convergence theorem by an extragradient method for variational inequality, equilibrium and fixed point problems", Bull. Malays. Math. Sci. Soc, 32(2), pp.173~185 (2009)
  17. D. Kinderlehrer, "An Introduction to Variational Inequalities and their Applications" (1980), Academic Press
  18. F. Kohsaka, "Fixed point theorems for a class of nonlinear map-pings related to maximal monotone operators in Banach spaces", Arch. Math. (Basel), 91(2), pp.166~177 (2008)
  19. W. R. Mann, "Mean value methods in iteration", Proc. Amer. Math. Soc, 4, pp.506~510 (1953)
  20. T. Maruyama, "Fixed point and mean ergodic theorems for new nonlinear mappings in Hilbert spaces", J. Nonlinear Convex Anal, 12(1), pp.185~197 (2011)
  21. A. Moudafi, "Lec-ture Notes in Econom. and Math. Systems, 477", pp.187~201 (1999), Springer
  22. S. Plubtieng, "Weak convergence theorem for monotone mappings and a countable family of nonexpansive mappings", J. Comput. Appl. Math, 224(2), pp.614~621 (2009)
  23. X. Qin, "Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces", J. Comput. Appl. Math, 225(1), pp.20~30 (2009)
  24. S. Takahashi, "Viscosity approximation methods for equilibrium prob-lems and fixed point problems in Hilbert spaces", J. Math. Anal. Appl, 331(1), pp.506~515 (2007)
  25. W. Takahashi, "Introduction to Nonlinear and Convex Analysis" (2009), Yokohoma Publishers
  26. W. Takahashi, "Fixed point theorems for new nonlinear mappings in a Hilbert space", J. Non-linear Convex Anal, 11(1), pp.79~88 (2010)
  27. W. Takahashi, "Weak convergence theorems for nonexpansive mappings and monotone mappings", J. Optim. Theory Appl, 118(2), pp.417~428 (2003)
  28. W. Takahashi, "Strong convergence theorems by hybrid methods for equilibrium problems and relatively nonexpansive mapping", Fixed Point Theory Appl, 2008, pp.11~ (2008)
  29. Fangfang Yan, "Convergence of Ishikawa'method for generalized hybrid mappings", 대한수학회논문집, 28(1), pp.135~141 (2013), 대한수학회

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