Iterative algorithms for variational inclusions, mixed equilibrium and fixed point problems with application to optimization problems
Yonghong Yao, Yeol Je Cho, Yeong‐Cheng Liou · Open Mathematics · 2011
Abstract In this paper, we introduce an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of a nonexpansive mapping, and the the set of solutions of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets, which is a solution of a certain optimization problem related to a strongly positive bounded linear operator.