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Zbl 1198.47082
Chang, Shih-Sen; Lee, H.W.Joseph; Chan, Chi Kin
A new method for solving equilibrium problem fixed point problem and variational inequality problem with application to optimization. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 9, A, 3307-3319 (2009). ISSN 0362-546X

From the summary: We introduce a new iterative scheme for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed point for a family of infinitely nonexpansive mappings and the set of solutions of the variational inequality for $\alpha$-inverse-strongly monotone mappings in a Hilbert space. Under suitable conditions, some strong convergence theorems for approximating a common element of the above three sets are obtained. As applications, at the end of the paper we utilize our results to study the optimization problem and some convergence problem for strictly pseudocontractive mappings.

MSC 2000:: *47J25 Methods for solving nonlinear operator equations (general)
47J20 Inequalities involving nonlinear operators
47H09 Mappings defined by "shrinking" properties
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: viscosity approximation method; equilibrium problem; fixed point; family of infinitely nonexpansive mappings; $\alpha $-inverse-strongly monotone mapping

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Zentralblatt MATH Berlin [Germany]