Forward-Backward Method with Nonquadratic Kernel for finding a Zero of a Sum of two Maximal Monotone Operators

An extension of the (nonexact-perturbed) forward-backward method for finding a zero of a sum of two maximal monotone operators is proposed, using a nonlinear metric, tied to Bregman functions. Results of weak and strong convergence for a sequence generated by such a method are established, under similar assumptions to those appearing in the context of the proximal point algorithm.