On the contraction‐proximal point algorithms with multi‐parameters

In this paper we consider the contraction‐proximal point algorithm: $x_{n+1}={\alpha }_{\mathrm{nu}}+{\lambda }_n{x}_n+{\gamma }_n{J}_{{\beta }_n}{x}_n,$ where $J_{{\beta }_n}$ denotes the resolvent of a monotone operator A. Under the assumption that lim n α n = 0, Σ n α n = ∞, lim inf n β n > 0, and lim inf n γ 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.