Modified Mann-Type Algorithm for Two Countable Families of Nonexpansive Mappings and Application to Monotone Inclusion and Image Restoration Problems

Author:

Ungchittrakool Kasamsuk12ORCID,Plubtieng Somyot12ORCID,Artsawang Natthaphon12ORCID,Thammasiri Purit1ORCID

Affiliation:

1. Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

2. Research Center for Academic Excellence in Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Abstract

In this paper, we introduce and study a modified Mann-type algorithm that combines inertial terms for solving common fixed point problems of two countable families of nonexpansive mappings in Hilbert spaces. Under appropriate assumptions on the sequences of parameters, we establish a strong convergence result for the sequence generated by the proposed method in finding a common fixed point of two countable families of nonexpansive mappings. This method can be applied to solve the monotone inclusion problem. Additionally, we employ a modified Mann-type iterative algorithm to address image restoration problems. Furthermore, we present numerical results across different scenarios to demonstrate the superior efficiency of our algorithm compared to existing algorithms.

Funder

National Research Council of Thailand

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Reference42 articles.

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5. Bauschke, H.H., and Combettes, P.L. (2011). Convex Analysis and Monotone Operator Theory in Hilbert Spaces. CMS Books in Mathematics, Springer.

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