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A viscosity approximation method for equilibrium problems, fixed point problems of nonexpansive mappings and a general system of variational inequalities

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Abstract

In this paper, we introduce and study a new iterative scheme for finding the common element of the set of common fixed points of a sequence of nonexpansive mappings, the set of solutions of an equilibrium problem and the set of solutions of the general system of variational inequality for α and μ-inverse-strongly monotone mappings. We show that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions. This main theorem extends a recent result of Ceng et al. (Math Meth Oper Res 67:375–390, 2008) and many others.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000, Thailand

    S. Plubtieng & T. Thammathiwat

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  1. S. Plubtieng
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  2. T. Thammathiwat
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Correspondence to S. Plubtieng.

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Plubtieng, S., Thammathiwat, T. A viscosity approximation method for equilibrium problems, fixed point problems of nonexpansive mappings and a general system of variational inequalities. J Glob Optim 46, 447–464 (2010). https://doi.org/10.1007/s10898-009-9448-5

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  • DOI: https://doi.org/10.1007/s10898-009-9448-5

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