The equilibrium problem defined by the Nikaidô–Isoda–Fan inequality contains a number of problems such as optimization, variational inequality, Kakutani fixed point, Nash equilibria, and others special cases. This paper presents picture for relationship between points Moreau proximal mapping solutions that satisfies some kinds monotonicity Lipschitz-type condition.

We consider a coefficient inverse problems for one model of HIV infection. The problem is formulated as an minimization problem of a quadratic residual functional. The last one is turned to the fixed point problem. We study two approaches to obtaining approximations such as the adaptive Wegstein method to solutions of the fixed point problem. One way is the vector approach, this method uses the...

In this paper, we propose an iterative algorithm for finding a common solution of a system of generalized equilibrium problems, a split equilibrium problem and a hierarchical fixed point problem over the common fixed points set of a finite family of nonexpansive mappings in Hilbert spaces. Furthermore, we prove that the proposed iterative method has strong convergence under some mild conditions...