AN ITERATIVE ALGORITHM FOR GENERALISED MIXED EQUILIBRIUM PROBLEMS, VARIATIONAL INEQUALITY PROBLEMS AND OPTIMISATION PROBLEMS

Jong Soo Jung

Abstract


In this paper, we consider a general composite iterative algorithm for finding a common element of the set of solutions of a generalised mixed equilibrium problem, the set of fixed points of an infinite family of non-expansive mappings and the set of solutions of a variational inequality problem for an inverse-strongly monotone mapping in Hilbert spaces. It is shown that the sequence generated by the proposed iterative scheme converges strongly to a common element of the above three sets under suitable control conditions, which solves a certain optimisation problem. The results of this article substantially improve, develop, and complement the previous well-known results in this area.


Keywords


Generalised mixed equilibrium problem; Fixed point; Non-expansive mapping; Inverse-strongly monotone mapping; Variational inequality; Optimisation problem; Metric projection; Strongly positive bounded linear operator



DOI: http://dx.doi.org/10.37569/DalatUniversity.2.2.201(2012)

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