On the contraction-proximal point algorithms with multi-parameters

In this paper we consider the contraction-proximal point algorithm: ${x_{n+1}=\alpha_nu+\lambda_nx_n+\gamma_nJ_{\beta_n}x_n,}$ where ${J_{\beta_n}}$ denotes the resolvent of a monotone operator A. Under the assumption that lim _n ??? _n ?=?0, ?? _n ??? _n ?=???, lim inf _n ??? _n ?>?0, and lim inf _n ?? _n ?> 0, we prove the strong convergence of the iterates as well as its inexact version. As a result we improve and recover some recent results by Boikanyo and Morosanu.