  This Note is inspired by the recent paper by Djafary Rouhani and Moradi [J.
Optim. Theory Appl. 172 (2017) 222-235], where a proximal point algorithm
proposed by Boikanyo and Moro\c{s}anu [Optim. Lett. 7 (2013) 415-420] is
discussed. We start with a brief history of the subject and then propose and
analyse the following more general algorithm for approximating the zeroes of a
maximal monotone operator $A$ in real Hilbert space $H$ $$
x_{n+1}=(I+\beta_nA)^{-1}(u_n + \alpha_n(x_n+e_n)), \ \ n\ge 0\, , $$ where
$x_0\in H$ is a given starting point, $u_n \rightarrow u$ is a given sequence
in $H$, ${R} \ni \alpha_n \rightarrow 0$, and $(e_n)$ is the error sequence
satisfying $\alpha_ne_n\rightarrow 0$. Besides the main result on the strong
convergence of $(x_n)$, we discuss some particular cases, including the
approximation of minimizers of convex functionals, explain how to use our
algorithm in practice, and present some simulations to illustrate the
applicability of our algorithm.
