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

Kasamsuk Ungchittrakool, Somyot Plubtieng, Natthaphon Artsawang () and Purit Thammasiri
Additional contact information
Kasamsuk Ungchittrakool: Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
Somyot Plubtieng: Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
Natthaphon Artsawang: Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
Purit Thammasiri: Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Mathematics, 2023, vol. 11, issue 13, 1-21

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.

Keywords: modified Mann-type algorithm; nonexpansive mapping; common fixed point problem; monotone inclusion problem; image restoration problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/13/2927/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/13/2927/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:13:p:2927-:d:1183039

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().