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Weak Convergence Theorems for Strictly Pseudocontractive Mappings and Generalized Mixed Equilibrium Problems

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  • Jong Soo Jung

Abstract

We introduce a new iterative method for finding a common element of the set of fixed points of a strictly pseudocontractive mapping, the set of solutions of a generalized mixed equilibrium problem, and the set of solutions of a variational inequality problem for an inverse-strongly-monotone mapping in Hilbert spaces and then show that the sequence generated by the proposed iterative scheme converges weakly to a common element of the above three sets under suitable control conditions. The results in this paper substantially improve, develop, and complement the previous well-known results in this area.

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  • Jong Soo Jung, 2012. "Weak Convergence Theorems for Strictly Pseudocontractive Mappings and Generalized Mixed Equilibrium Problems," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-18, June.
    • Handle: RePEc:hin:jnljam:384108
    DOI: 10.1155/2012/384108
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