Iterative method for fixed point problem, variational inequality and generalized mixed equilibrium problems with applications

Iterative method for fixed point problem, variational inequality and generalized mixed equilibrium problems with applications

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Article ID: iaor201113483
Volume: 52
Issue: 1
Start Page Number: 57
End Page Number: 77
Publication Date: Jan 2012
Journal: Journal of Global Optimization
Authors:
Keywords: calculus of variations
Abstract:

In this paper, we introduce a new iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solution of generalized mixed equilibrium problem and the set of solutions of the variational inequality problem for a co‐coercive mapping in a real Hilbert space. Then strong convergence of the scheme to a common element of the three sets is proved. Furthermore, new convergence results are deduced and finally we apply our results to solving optimization problems and present other applications.

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