Abstract
In this works, by using the modified viscosity approximation method associated with Meir-Keeler contractions, we proved the convergence theorem for solving the fixed point problem of a nonexpansive semigroup and generalized mixed equilibrium problems in Hilbert spaces.
Highlights
As you know, there are many problems that are reduced to find solutions of equilibrium problems which cover variational inequalities, fixed point problems, saddle point problems, complementarity problems as special cases
Equilibrium problem which was first introduced by Blum and Oettli [1] has been extensively studied as effective and powerful tools for a wide class of real world problems, which arises in economics, finance, image reconstruction, ecology, transportation network and related optimization problems
The so-called generalized mixed equilibrium problem has been investigated by many authors [2] [3]
Summary
There are many problems that are reduced to find solutions of equilibrium problems which cover variational inequalities, fixed point problems, saddle point problems, complementarity problems as special cases. Let denote F (T ) the set of fixed points of the mapping T. In 1967, Halpern [14] introduced the following iterative method for a nonexpansive mapping T : K → K in a real Hilbert space, for finding x1 ∈ K and xn+1= αnu + (1−αn )Txn , n ≥ 1 (1.7)
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