  We consider the convergence behavior using the relaxed Peaceman-Rachford
splitting method to solve the monotone inclusion problem $0 \in (A + B)(u)$,
where $A, B: \Re^n \rightrightarrows \Re^n$ are maximal $\beta$-strongly
monotone operators, $n \geq 1$ and $\beta > 0$. Under a technical assumption,
convergence of iterates using the method on the problem is proved when either
$A$ or $B$ is single-valued, and the fixed relaxation parameter $\theta$ lies
in the interval $(2 + \beta, 2 + \beta + \min \{ \beta, 1/\beta \})$. With this
convergence result, we address an open problem that is not settled in [20] on
the convergence of these iterates for $\theta \in (2 + \beta, 2 + \beta + \min
\{ \beta, 1/\beta\})$. Pointwise convergence rate results and $R$-linear
convergence rate results when $\theta$ lies in the interval $[2 + \beta, 2 +
\beta + \min \{ \beta, 1/\beta\})$ are also provided in the paper. Our analysis
to achieve these results is atypical and hence novel. Numerical experiments are
conducted on the weighted Lasso minimization problem to test the validity of
the assumption .
