Tseng’s Algorithm with Extrapolation from the past Endowed with Variable Metrics and Error Terms

In this paper, we propose a variable metric version of Tseng’s algorithm (the forward-backward-forward algorithm: FBF) combined with extrapolation from the past that includes error terms for finding zero sum maximally monotone operator and Lipschitzian in Hilbert spaces. The algorithm, which is modified forward-reflected-backword method, endowed metrics terms. Primal-dual algorithms are also proposed inclusion problems involving compositions linear operators. primal-dual problem occurring image deblurring demonstrates an application our theoretical results.