The aim of this paper is to prove a strong convergence result for an algorithm introduced by Y. Yao and M. A. Noor in 2008 under a new condition on one of the parameters involved. Further, convergence properties of a generalized proximal point algorithm which was introduced in [5] are analyzed. The results in this paper are proved under the general condition that errors tend to zero in norm. These results extend and improve several previous results on the regularization method and the proximal point algorithm.