Abstract
In this paper, we introduce an iterative method for finding a common element of the set of fixed points of nonexpansive mappings, the set of solutions of a finite family of variational inclusions with set-valued maximal monotone mappings and inverse strongly monotone mappings, and the set of solutions of an equilibrium problem in Hilbert spaces. Furthermore, using our new iterative scheme, under suitable conditions, we prove some strong convergence theorems for approximating these common elements. The results presented in the paper improve and extend many recent important results.
Highlights
Let H be a real Hilbert space whose inner product and norm are denoted by ·, · and ·, respectively
Let C be a nonempty closed convex subset of H, and let F be a bifunction of C × C into R which is the set of real numbers
The classical variational inequality which is denoted by VI(A, C) is to find x ∈ C such that
Summary
Let H be a real Hilbert space whose inner product and norm are denoted by ·, · and · , respectively. In , Tian [ ] introduced the following general iterative scheme for finding an element of the set of solutions to the fixed point of a nonexpansive mapping in a Hilbert space: Define the sequence {xn} by xn+ = αnγ f (xn) + (I – μαnB)Txn, n ≥ ,
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