Abstract
The strong convergence theorem is proved for finding a common solution for a system of equilibrium problems: find where is a closed convex subset of a Hilbert space and are bifunctions from into R given exactly or approximatively. As an application, finding a common solution for a system of variational inequality problems is given.
Highlights
Let H be a real Hilbert space with the scalar product and the norm denoted by the symbols ·, · and ·, respectively
We consider the system of equilibrium problems: find u∗ ∈ S : ∩Ni 1EP Fi, 1.1
When F1 u, v A1 u, v − u where A1 is a monotone operator, 1.1 is a problem of finding an element which is a solution of a variational inequality problem and a common fixed point for a finite family of strictly pseudocontractive mappings and investigated intensively in 20–32
Summary
Let H be a real Hilbert space with the scalar product and the norm denoted by the symbols ·, · and · , respectively. The bifunction F satisfies the following conditions: A1 F u, u 0 for all u ∈ C.
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