A Halpern Method for Solving Perturbed Double Inertial Krasnoselskii-Mann Iterations with Applications to Image Restoration Problems

Rattanaporn Wangkeeree; Rabian Wangkeeree; Yirga Abebe Belay; Kasamsuk Ungchittrakool; Purit Thammasiri; Pakkapon Preechasilp

doi:10.58715/bangmodjmcs.2025.11.16

Authors

Rattanaporn Wangkeeree Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
Rabian Wangkeeree Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand https://orcid.org/0000-0002-5715-3804
Yirga Abebe Belay Department of Mathematics, Aksum University, P.O. Box 1010, Axum, Ethiopia https://orcid.org/0000-0002-6112-2154
Kasamsuk Ungchittrakool Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
Purit Thammasiri Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand https://orcid.org/0009-0007-3918-124X
Pakkapon Preechasilp Department of Mathematics, Pibulsongkram Rajabhat University, Phitsanulok 65000, Thailand https://orcid.org/0000-0003-2826-2742

DOI:

https://doi.org/10.58715/bangmodjmcs.2025.11.16

Keywords:

Fixed points, inertial iteration, perturbation parameters, quasi--nonexpansive mappings, Strong convergence

Abstract

In this paper, we introduce and study a Halpern inertial method for solving the general perturbed Krasnoselskii-Mann type algorithm in Hilbert space settings, where the underlying mapping is quasi-nonexpansive. We discuss convergence analysis of the method under some mild assumptions on the control sequences. We additionally present a numerical example to demonstrate the effectiveness of the method. Finally, we apply the method in solving image restoration problems. We evaluate the quality of the improvement in the Signal-to-Noise Ratio (ISNR) and the restored images using the Structural Similarity Index Measure (SSIM) metrics. The results of this work generalize and expand upon numerous results found in the literature.