Kunrada KankamPrasit Cholamjiak2025-07-072025-07-072025Discrete and Continuous Dynamical Systems - Series S1937163210.3934/dcdss.20241162-s2.0-105008722493https://repository.dusit.ac.th/handle/123456789/7310This research presents the projection forward-backward-forward method based on two inertials. We combine linesearch and self-adaptive stepsize to select the stepsize in the proposed method. The weak convergence is established under mild assumptions without the assumptions on the Lipschitz constants. Finally, numerical experiments are performed, which explain the effectiveness of the proposed method. We provide practical applications in image inpainting problem. The results of our numerical analysis conclusively indicate that the proposed method exhibits greater efficiency than those previously recommended in literature. © 2025 American Institute of Mathematical Sciences. All rights reserved.Forward-backward-forward methodimage inpaintinginertial methodmonotone inclusionArticleScopus