Abstract
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 α n = 0, ∑ 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.
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Wang, F., Cui, H. On the contraction-proximal point algorithms with multi-parameters. J Glob Optim 54, 485–491 (2012). https://doi.org/10.1007/s10898-011-9772-4
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DOI: https://doi.org/10.1007/s10898-011-9772-4