An improved fast iterative shrinkage thresholding algorithm with an error for image deblurring problem

Abstract In this paper, we introduce a new iterative forward-backward splitting method with an error for solving the variational inclusion problem of sum two monotone operators in real Hilbert spaces. We suggest and analyze under some mild appropriate conditions imposed on parameters such that another strong convergence theorem these is obtained. also apply our main result to improve fast shrinkage thresholding algorithm (IFISTA) image deblurring problem. Finally, provide numerical experiments illustrate behavior show effectiveness sequence constructed by inertial technique processing high performance good IFISTA.