Algorithms for approximating minimization problems in Hilbert spaces

In this paper, we study the following minimization problem minx∈Fix(S)∩Ωμ2〈Bx,x〉+12‖x‖2−h(x), where BB is a bounded linear operator, μ≥0μ≥0 is some constant, hh is a potential function for γ̄f, Fix(T)Fix(T) is the set of fixed points of nonexpansive mapping SS and ΩΩ is the solution set of an equilibrium problem. This paper introduces two new algorithms (one implicit and one explicit) that can be used to find the solution of the above minimization problem.