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Ge, Ci-Shui; Yu, Neng-Fu; Zhao, Lin

Strong convergence of iterative algorithms with variable coefficients for generalized equilibrium problems, variational inequality problems and fixed point problems. (English) Zbl 1476.47052

Fixed Point Theory Appl. 2013, Paper No. 257, 18 p. (2013).
Summary: In this paper, we propose some new iterative algorithms with variable coefficients for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping and the set of common fixed points of a finite family of asymptotically \(\kappa\)-strict pseudocontractive mappings in the intermediate sense. Some strong convergence theorems of these iterative algorithms are obtained without some boundedness conditions which are not easy to examine in advance. The results of the paper improve and extend some recent ones announced by many others. The algorithms with variable coefficients introduced in this paper are of independent interests.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.

Keywords:

generalized equilibrium problem; variational inequality; fixed point; asymptotically strict pseudocontractive mapping in the intermediate sense; algorithm with variable coefficients; strong convergence
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