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Zbl 1186.47075
Plubtieng, Somyot; Sriprad, Wanna
A viscosity approximation method for finding common solutions of variational inclusions, equilibrium problems, and fixed point problems in Hilbert spaces. (English)
[J] Fixed Point Theory Appl. 2009, Article ID 567147, 20 p. (2009). ISSN 1687-1812/e

Summary: We introduce an iterative method for finding a common element of the set of common fixed points of a countable family of nonexpansive mappings, the set of solutions of a variational inclusion with set-valued maximal monotone mapping, and inverse strongly monotone mappings and the set of solutions of an equilibrium problem in Hilbert spaces. Under suitable conditions, some strong convergence theorems for approximating these common elements are proved. The results presented in the paper improve and extend the main results of {\it J.\,W.\thinspace Peng, Y.\,Wang, D.\,S.\thinspace Shyu} and {\it J.-C.\thinspace Yao} [J.~Inequal.\ Appl.\ 2008, Article ID 720371 (2008; Zbl 1161.65050)] and many others.

MSC 2000:: *47J25 Methods for solving nonlinear operator equations (general)
47H09 Mappings defined by "shrinking" properties
47H05 Monotone operators (with respect to duality)
47J22

Citations: Zbl 1161.65050

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