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We establish definitions for left and right coordinate convexity and demonstrate both weak and strong convergence results based on reasonable assumptions. Furthermore, our algorithm\u2019s effectiveness in solving the heat equation is highlighted, contributing to energy optimization and sustainable development.<\/jats:p>","DOI":"10.3390\/axioms13110729","type":"journal-article","created":{"date-parts":[[2024,10,22]],"date-time":"2024-10-22T04:10:14Z","timestamp":1729570214000},"page":"729","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["An Iterative Approach to Common Fixed Points of G-Nonexpansive Mappings with Applications in Solving the Heat Equation"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0790-3811","authenticated-orcid":false,"given":"Raweerote","family":"Suparatulatorn","sequence":"first","affiliation":[{"name":"Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand"},{"name":"Centre of Excellence in Mathematics, MHESI, Bangkok 10400, Thailand"},{"name":"Office of Research Administration, Chiang Mai University, Chiang Mai 50200, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7445-1734","authenticated-orcid":false,"given":"Payakorn","family":"Saksuriya","sequence":"additional","affiliation":[{"name":"Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand"},{"name":"Centre of Excellence in Mathematics, MHESI, Bangkok 10400, Thailand"},{"name":"International College of Digital Innovation, Chiang Mai University, Chiang Mai 50200, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Teeranush","family":"Suebcharoen","sequence":"additional","affiliation":[{"name":"Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand"},{"name":"Centre of Excellence in Mathematics, MHESI, Bangkok 10400, Thailand"},{"name":"Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3246-673X","authenticated-orcid":false,"given":"Khuanchanok","family":"Chaichana","sequence":"additional","affiliation":[{"name":"Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, Thailand"},{"name":"Centre of Excellence in Mathematics, MHESI, Bangkok 10400, Thailand"},{"name":"Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Dudorova, N.V., and Belan, B.D. 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