Iterative algorithms for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of families and semigroups of nonexpansive mappings

作者：Saeidi Shahram^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2009, 70(12): 4195-4208.

DOI：10.1016/j.na.2008.09.009

• Amenable semigroup
• Common fixed point
• Equilibrium problem
• Iterative algorithm
• Nonexpansive mapping
• Projection
• Variational inequality
• Viscosity approximation

We introduce iterative algorithms for finding a common element of the set of solutions of a system of equilibrium problems and of the set of fixed points of a finite family and a left amenable semigroup of nonexpansive mappings in a Hilbert space. We prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. Our results extend, for example, the recent result of [V. Colao, G. Marino, H.K. Xu, An Iterative Method for finding common solutions of equilibrium and fixed point problems, J. Math. Anal. Appl. 344 (2008) 340-352] to systems of equilibrium problems.

• 出版日期2009-6-15