Strong convergence theorems for equilibrium problems and fixed point problems: A new iterative method, some comments and applications

Abstract

Abstract In this paper, we introduce a new approach method to find a common element in the intersection of the set of the solutions of a finite family of equilibrium problems and the set of fixed points of a nonexpansive mapping in a real Hilbert space. Under appropriate conditions, some strong convergence theorems are established. The results obtained in this paper are new, and a few examples illustrating these results are given. Finally, we point out that some 'so-called' mixed equilibrium problems and generalized equilibrium problems in the literature are still usual equilibrium problems. 2010 Mathematics Subject Classification: 47H09; 47H10, 47J25.

Keywords

• strong convergence
• iterative method
• equilibrium problem
• fixed point problem