WEAK CONVERGENCE THEOREMS FOR GENERALIZED MIXED EQUILIBRIUM PROBLEMS, MONOTONE MAPPINGS AND PSEUDOCONTRACTIVE MAPPINGS
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In this paper, we introduce a new iterative algorithm for finding a common element of the set of solutions of a generalized mixed equilibrium problem related to a continuous monotone mapping, the set of solutions of a variational inequality problem for a continuous monotone mapping, and the set of fixed points of a continuous pseudocontractive mapping in Hilbert spaces. Weak convergence for the proposed iterative algorithm is proved. Our results improve and extend some recent results in the literature.
Abstract
In this paper, we introduce a new iterative algorithm for finding a common element of the set of solutions of a generalized mixed equilibrium problem related to a continuous monotone mapping, the set of solutions of a variational inequality problem for a continuous monotone mapping, and the set of fixed points of a continuous pseudocontractive mapping in Hilbert spaces. Weak convergence for the proposed iterative algorithm is proved. Our results improve and extend some recent results in the literature.
참고문헌 (35)
- G. L. Acedo, "Iterative methods for strict pseudo-contractions in Hilbert spaces", Nonlinear Anal, 67(7), pp.2258~2271 (2007)
- R. P. Agarwal, "Fixed Point Theory for Lipschitzian-Type Mappings with Applications" (2009), Springer
- E. Blum, "From optimization and variational inequalities to equilibrium problems", Math. Student, 63, pp.123~145 (1994)
- Abdellah Bnouhachem, "An iterative algorithm for system of generalized equilibrium problems and fixed point problem", Fixed Point Theory and Applications, 2014(1), pp.235~ (2014), Springer Nature[DOI]
- L.-C. Ceng, "An iterative scheme for equi-librium problems and fixed point problems of strict pseudo-contraction mappings", J. Comput. Appl. Math, 223(2), pp.967~974 (2009)
- 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)
- T. Chamnarnpan, "A new iterative method for a common solution of a fixed points for pseudo-contractive mappings and variational inequalities", Fixed Point Theory Appl, 2012, pp.6~ (2012)[DOI]
- C. E. Chidume, "An example of the Mann iteration method for Lipschitz pseudocontractions", Proc. Amer. Math. Soc, 129(8), pp.2359~2363 (2001)
- Y. J. Cho, "Some results on k-strictly pseudo-contractive map-pings in Hilbert spaces", Nonlinear Anal, 70(5), pp.1956~1964 (2009)
- P. I. Combettes, "Equilibrium programming in Hilbert spaces", J. Nonlinear Convex Anal, 6(1), pp.117~136 (2005)
- S. D. Flam, "Equilibrium programming using proximal-like algorithm", Math. Program, 78(1), pp.29~41 (1997)
- H. Iiduka, "Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings", Nonlinear Anal, 61(3), pp.341~350 (2005)
- J. S. Jung, "Strong convergence of composite iterative methods for equilibrium problems and fixed point problems", Appl. Math. Comput, 213(2), pp.498~505 (2009)
- J. S. Jung, "Strong convergence of iterative methods for k-strictly pseudo-contractive map-pings in Hilbert spaces", Appl. Math. Comput, 215(10), pp.3746~3753 (2010)
- J. S. Jung, "it A new iteration method for nonexpansive mappings and monotone map-pings in Hilbert spaces", J. Inequal. Appl, 2010, pp.16~ (2010)[DOI]
- J. S. Jung, "Some results on a general iterative method for k-strictly pseudo-contractive mappings", Fixed Point Theory Appl, 2011, pp.11~ (2011)
- Jong Soo Jung, "A general composite iterative method for generalized mixed equilibrium problems, variational inequality problems and optimization problems", Journal of Inequalities and Applications, 2011(1), pp.51~ (2011), Springer Nature[DOI]
- J. S. Jung, "Weak convergence theorems for strictly pseudocontractive mappings and gen-eralized mixed equilbrium problems", J. Appl. Math, 2012, pp.18~ (2012)[DOI]
- J. S. Jung, "Iterative methods for pseudocontractive mappings in Banach spaces", Abstr. Appl. Anal, 2013, pp.7~ (2013)[DOI]
- P. Katchang, "Strong convergence theorems for solving generalized mixed equilibrium problems and general system of variational inequalities by the hybrid method", Nonlinear Anal. Hybrid Syst, 4(4), pp.838~852 (2010)
- P. Kumam, "Common solutions of generalized mixed equilibrium problems, variational inclusions, and common fixed points for nonexpan-sive semigroups and strictly pseudocontractive mappings", J. Appl. Math, 2011, pp.28~ (2011)
- G. Marino, "Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces", J. Math. Anal. Appl, 329(1), pp.336~346 (2007)
- C. H. Morales, "Strong convergence of path for continuous pseudo-contractive mappings", Proc. Amer. Math. Soc, 135(9), pp.2831~2838 (2007)
- C. H. Morales, "Convergence of paths for pseudo-contractive mappings in Banach spaces", Proc. Amer. Math. Soc, 128(11), pp.3411~3419 (2000)
- A. Moudafi, "Weak convergence theorems for nonexpansive mappings and equilibrium problems", J. Nonlinear Convex Anal, 9(1), pp.37~43 (2008)
- J.-W. Peng, "A new Hybrid-extragradient method for generalized mixed equilibrium problems, fixed point problems and variational inequality problems", Tai-wanese J. Math, 12(6), pp.1401~1432 (2008)
- 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)
- J. Schu, "Weak and strong convergence to fixed points of asymptotically nonexpansive mappings", Bull. Aust. Math. Soc, 43(1), pp.153~159 (1991)
- A. Tada, "Weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem", J. Optim. Theory Appl, 133(3), pp.359~370 (2007)
- S. Takahashi, "Strong convergence theorem for a generalized equi-librium problem and a nonexpansive mapping in a Hilbert space", Nonlinear Anal, 69(3), pp.1025~1033 (2008)
- W. Takahashi, "Weak convergence theorems for nonexpansive mappings and monotone mappings", J. Optim. Theory Appl, 118(2), pp.417~428 (2003)
- Y. H. Yao, "Mixed equilibrium problems and optimization problems", J. Math. Anal. Appl, 354(1), pp.319~329 (2009)
- H. Zegeye, "An iterative approximation method for a common fixed point of two pseudo-contractive mappings", ISRN Math. Anal, 2011, pp.14~ (2011)
- S. Zhang, "Generalized mixed equilibrium problems in Banach spaces", Appl. Math. Mech. (English Ed.), 30(9), pp.1105~1112 (2009)
- H. Zhou, "Convergence theorems of fixed points for k-strict pseudo-contractions in Hilbert spaces", Nonlinear Anal, 69(2), pp.456~462 (2008)
