Description:
We prove that a large family of Fejer convergent iterative methods still converges to a solution when summable errors are incorporated to the algorithm. We define approximate resolvents, show that methods based on approximate resolvents fall within the aforementioned family and prove that approximate resolvents are the iteration maps of the hybrid proximal-extragradient method. We prove that the forward-backward splitting method, Tseng's modified forward-backward splitting method and Koreplevich method are all based in particular computations elements in approximate resolvents.