{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:21:08Z","timestamp":1760149268166,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,24]],"date-time":"2023-07-24T00:00:00Z","timestamp":1690156800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Chiang Mai University, Faculty of Science, Chiang Mai University"},{"name":"King Mongkut\u2019s University of Technology Thonburi"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this work, an algorithm is introduced for the problem of finding a common fixed point of a finite family of G-nonexpansive mappings in a real Hilbert space endowed with a directed graph G. This algorithm is a modified parallel algorithm inspired by the inertial method and the Mann iteration process. Moreover, both weak and strong convergence theorems are provided for the algorithm. Furthermore, an application of the algorithm to a signal recovery problem with multiple blurring filters is presented. Consequently, the numerical experiment shows better results compared with the previous algorithm.<\/jats:p>","DOI":"10.3390\/sym15071464","type":"journal-article","created":{"date-parts":[[2023,7,25]],"date-time":"2023-07-25T01:21:27Z","timestamp":1690248087000},"page":"1464","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Modified Parallel Algorithm for a Common Fixed-Point Problem with Application to Signal Recovery"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2508-1738","authenticated-orcid":false,"given":"Anchalee","family":"Khemphet","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mueang Chiang Mai, Chiang Mai University, Chiang Mai 50200, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0790-3811","authenticated-orcid":false,"given":"Raweerote","family":"Suparatulatorn","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mueang Chiang Mai, Chiang Mai University, Chiang Mai 50200, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3425-3447","authenticated-orcid":false,"given":"Pariwate","family":"Varnakovida","sequence":"additional","affiliation":[{"name":"KMUTT Geospatial Engineering and Innovation Center, Faculty of Science, King Mongkut\u2019s University of Technology Thonburi, Thung Khru, Bangkok 10140, Thailand"},{"name":"Department of Mathematics, Faculty of Science, King Mongkut\u2019s University of Technology Thonburi, Thung Khru, Bangkok 10140, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5063-1220","authenticated-orcid":false,"given":"Phakdi","family":"Charoensawan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mueang Chiang Mai, Chiang Mai University, Chiang Mai 50200, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1186\/s13663-015-0436-9","article-title":"On Browder\u2019s convergence theorem and Halpern iteration process for G-nonexpansive mappings in Hilbert spaces endowed with graphs","volume":"2015","author":"Tiammee","year":"2015","journal-title":"Fixed Point Theory Appl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1186\/s13663-016-0578-4","article-title":"Common fixed points of G-nonexpansive mappings on Banach spaces with a graph","volume":"2016","author":"Tripak","year":"2016","journal-title":"Fixed Point Theory Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2361","DOI":"10.1007\/s40840-018-0606-0","article-title":"Convergence analysis of SP-iteration for G-nonexpansive mappings with directed graphs","volume":"42","author":"Sridarat","year":"2019","journal-title":"Bull. 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