  A new framework for analyzing Fejer convergent algorithms is presented. Using
this framework we define a very general class of Fejer convergent algorithms
and establish its convergence properties. We also introduce a new definition of
approximations of resolvents which preserve some useful features of the exact
resolvent, and use this concept to present an unifying view of the
Forward-Backward splitting method, Tseng's Modified Forward-Backward splitting
method and Korpelevich's method. We show that methods based on families of
approximate resolvents fall within the aforementioned class of Fejer convergent
methods. We prove that such approximate resolvents are the iteration maps of
the Hybrid Proximal-Extragradient method.
