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

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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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  1. Mathematics Institute, African University of Science and Technology, Abuja, Nigeria

    Yekini Shehu

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  1. Yekini Shehu
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Shehu, Y. Iterative method for fixed point problem, variational inequality and generalized mixed equilibrium problems with applications. J Glob Optim 52, 57–77 (2012). https://doi.org/10.1007/s10898-011-9679-0

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  • DOI: https://doi.org/10.1007/s10898-011-9679-0

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