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In this paper, we introduce a new iterative method using an inertial technique for approximating a common fixed point of an infinite family of nonexpansive mappings in a Hilbert space. The proposed method’s weak convergence theorem was established under some suitable conditions. Furthermore, we applied our main results to solve convex minimization problems and image restoration problems.

A Fast Fixed-Point Algorithm for Convex Minimization Problems and Its Application in Image Restoration Problems