Strong convergence of iterative algorithms with variable coefficients for generalized equilibrium problems, variational inequality problems and fixed point problems

• Published in: Fixed point theory and applications (Hindawi Publishing Corporation) Vol. 2013; no. 1
• Main Authors: Ge, Ci-Shui, Yu, Neng-Fu, Zhao, Lin
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 07.11.2013
• Subjects: Analysis; Applications of Mathematics; Differential Geometry; Mathematical and Computational Biology; Mathematics; Mathematics and Statistics; Topology; algorithm with variable coefficients; variational inequality; asymptotically strict pseudocontractive mapping in the intermediate sense; generalized equilibrium problem; fixed point
• ISSN: 1687-1812; 1687-1820; 1687-1812
• DOI: 10.1186/1687-1812-2013-257

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 κ -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: 47H09, 47H10, 47J20.