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A viscosity approximation method for finding a common solution of fixed points and equilibrium problems in Hilbert spaces

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Abstract

In this paper, we introduce an iterative method for finding a common element of the set of fixed points of a nonexpansive mapping and the set of common fixed points of a countable family of nonexpansive mappings in Hilbert spaces. Using the result we consider a strong convergence theorem in variational inequalities and equilibrium problems. The result present in this paper extend and improve the corresponding result of Qin et al. (Nonlinear Anal 69:3897–3909, 2008), Plubtieng and Punpaeng (J Math Anal Appl 336:455–469, 2007) and many others.

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Authors and Affiliations

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

    Somyot Plubtieng & Tipphawan Thammathiwat

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  1. Somyot Plubtieng
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  2. Tipphawan Thammathiwat
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Correspondence to Somyot Plubtieng.

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Supported by The Royal Golden Jubilee Program under Grant PHD/0117/2549, Thailand.

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Plubtieng, S., Thammathiwat, T. A viscosity approximation method for finding a common solution of fixed points and equilibrium problems in Hilbert spaces. J Glob Optim 50, 313–327 (2011). https://doi.org/10.1007/s10898-010-9583-z

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  • DOI: https://doi.org/10.1007/s10898-010-9583-z

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