On the contraction-proximal point algorithms with multi-parameters

In this paper we consider the contraction-proximal point algorithm: <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${x_{n+1}=\alpha_nu+\lambda_nx_n+\gamma_nJ_{\beta_n}x_n,}$$< /EquationSource> </InlineEquation> where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${J_{\beta_n}}$$</EquationSource> </InlineEquation> denotes the resolvent of a monotone operator A. Under the assumption that lim<Subscript> n </Subscript> α <Subscript> n </Subscript> = 0, ∑<Subscript> n </Subscript> α <Subscript> n </Subscript> = ∞, lim inf<Subscript> n </Subscript> β <Subscript> n </Subscript> > 0, and lim inf<Subscript> n </Subscript> γ <Subscript> n </Subscript> > 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. Copyright Springer Science+Business Media, LLC. 2012