A proximal point algorithm with general errors

In this paper, we state and prove a strong convergence result associated with a proximal point algorithm introduced by Yao and Shahzad [Strong convergence of a proximal point algorithm with general errors, to appear in Optim. Lett.] under less restrictive conditions on the control parameters involved. Therefore, the main result of this paper improves significantly the main result of the above quoted paper. We also give a generalization of the well known lemma due to Xu [Iterative algorithms for nonlinear operators, J. London Math. Soc. 66 (2002), 240-256].