An Accelerated Fixed-Point Algorithm with an Inertial Technique for a Countable Family of G-Nonexpansive Mappings Applied to Image Recovery

Many authors have proposed fixed-point algorithms for obtaining a fixed point of G-nonexpansive mappings without using inertial techniques. To improve convergence behavior, some accelerated methods been introduced. The main aim this paper is to use coordinate affine structure create an algorithm with technique countable family in Hilbert space symmetric directed graph G and prove the weak theorem algorithm. As application, we apply our solve image restoration convex minimization problems. numerical experiments show that more efficient than FBA, FISTA, Ishikawa iteration, S-iteration, Noor iteration SP-iteration.