Strongly Convergent Inertial Krasnosel'skii–Mann and Ishikawa-Type Schemes for Fixed Point and Monotone Inclusion Problems with Applications to Image Restoration

We propose an inertial Krasnosel'skii–Mann and Ishikawa-type iterative process with step-size control for finding fixed points of nonexpansive mappings in Hilbert spaces. Without relying on viscosity-type techniques and under mild assumptions on the control parameters, we establish strong convergence of the scheme. The method is also utilized for solving monotone inclusion problems and extended to image restoration applications. Numerical tests on several blurring operators confirm that the algorithm attains higher signal-to-noise ratio (SNR), delivers superior restoration quality compared with existing approaches.