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Solutions of systems of variational inequalities on fixed points of nonexpansive mappings

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In this paper, we introduce a new approximating method for finding the common element of the set of fixed points of nonexpansive mappings and the set of solution of system variational inequalities for finite family of inverse strongly monotone mappings and strictly pseudo-contractive of Browder-Petryshyn type mappings. We show that the sequence converges strongly to a common element the above two sets under some parameter controling conditions. Our results improve and extend the results announced by many others.

Abstract

In this paper, we introduce a new approximating method for finding the common element of the set of fixed points of nonexpansive mappings and the set of solution of system variational inequalities for finite family of inverse strongly monotone mappings and strictly pseudo-contractive of Browder-Petryshyn type mappings. We show that the sequence converges strongly to a common element the above two sets under some parameter controling conditions. Our results improve and extend the results announced by many others.

참고문헌 (21)

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  3. L. C. Ceng, "A general iterative method with strongly positive operators for general variational inequalities", Comput. Math. Appl, 59(4), pp.14411452~ (2010)
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  6. T. Jitpeera, "A general iterative algorithm for generalized mixed equilibrium problems and variational inclusions approach to variational inequalities", Int. J. Math. Math. Sci, 2011, pp.25~ (2011)
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  10. G. Marino, "A general iterative method for nonexpansive mappings in Hilbert spaces", J. Math. Anal. Appl, 318(1), pp.43~52 (2006)
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  12. H. Piri, "A general iterative method for finding common solutions of system of equilibrium problems, system of variational inequalities and fixed point problems", Math. Comput. Modell, 55, pp.1622~1638 (2012)
  13. H. Piri, "Solutions of variational inequalities on fixed points of nonexpansive mappings", Bull. Iranian Math. Soc, 39(4), pp.743~764 (2013)
  14. H. Piri, "Hybrid pseudo-viscosity approximation schemes for systems of equilibrium prob-lems and fixed point problems of infinite family and semigroup of non-expansive map-pings", Nonlinear Anal, 74(17), pp.6788~6804 (2011)
  15. H. Piri, "Strong convergence for a minimization problem on solutions of systems of equilibrium problems and common fixed points of an infinite family and semigroup of nonexpansive mappings", Comput. Math. Appl, 61(9), pp.2562~2577 (2011)
  16. H. Piri, "Strong convergence theorem for amenable semigroups of non-expansive mappings and variational inequalities", Fixed Point Theory Appl, 2011 (2011)[DOI]
  17. S. Plubtieng, "Strong convergence theorems for three-step iterations with errors for non-lipschitzian nonself-mappings in Banach spaces", Comput. Math. Appl, 51(6-7), pp.1093~1102 (2006)
  18. R. T. Rockafellar, "On the maximality of sums of nonlinear monotone operators", Trans. Amer. Math. Soc, 149, pp.75~88 (1970)
  19. N. Xiu, "Modified fixed-point equations and related iterative methods for variational inequalities", Comput. Math. Appl, 47(6-7), pp.913~920 (2004)
  20. H. K. Xu, "An iterative approach to quadratic optimization", J. Optim. Theory Appl, 116(3), pp.659~678 (2003)
  21. Y. Yao, "On modified iterative method for nonexpansive mappings and monotone mappings", Appl. Math. Comput, 186(2), pp.1551~1558 (2007)

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