  In this paper, we propose an improved iterative method for solving the
monotone inclusion problem in the form of $0 \in Ax + Dx + N_{C}(x)$ in real
Hilbert space, where $A$ is a maximally monotone operator, $D$ and $B$ are
monotone and Lipschitz continuous, and $C$ is the nonempty set of zeros of the
operator $B$. Our investigated method, called Tseng's forward-backward-forward
with extrapolation from the past and penalty scheme, extends the one proposed
by Bot and Csetnek [Set-Valued Var. Anal. 22: 313--331, 2014]. We investigate
the weak ergodic and strong convergence (when $A$ is strongly monotone) of the
iterates produced by our proposed scheme. We show that the algorithmic scheme
can also be applied to minimax problems. Furthermore, we discuss how to apply
the method to the inclusion problem involving a finite sum of compositions of
linear continuous operators by using the product space approach and employ it
for convex minimization. Finally, we present a numerical experiment in TV-based
image inpainting to validate the proposed theoretical theorem.
