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Let H be a real Hilbert space. Consider on H a nonexpansive family T={T(t):0≤t<∞}Open image in new window with a common fixed point, a contraction f with the coefficient 0 < α < 1, and a strongly positive linear bounded self-adjoint operator A with the coefficient γ̄>0Open image in new window. Assume that 0<γ<γ̄/αOpen image in new window and that S={St:0≤t<∞}Open image in new window is a family of nonexpansive self-mappings on H such that F(T)⊆F(S)Open image in new window and  Open image in new window  has property (A)Open image in new window with respect to the family  Open image in new window . It is proved that the following schemes (one implicit and one inexact explicit):

A general inexact iterative method for monotone operators, equilibrium problems and fıxed point problems of semigroups in Hilbert spaces