{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,19]],"date-time":"2025-12-19T09:58:40Z","timestamp":1766138320966,"version":"build-2065373602"},"reference-count":45,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,6,5]],"date-time":"2023-06-05T00:00:00Z","timestamp":1685923200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12071316","cstc2021jcyj-msxmX0177"],"award-info":[{"award-number":["12071316","cstc2021jcyj-msxmX0177"]}]},{"name":"Natural Science Foundation of Chongqing","award":["12071316","cstc2021jcyj-msxmX0177"],"award-info":[{"award-number":["12071316","cstc2021jcyj-msxmX0177"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this work, we consider the monotone inclusion problem in real Hilbert spaces and propose a simple inertial method that does not include any evaluations of the associated resolvent and projection. Under suitable assumptions, we establish the strong convergence of the method to a minimal norm solution. Saddle points of minimax problems and critical points problems are considered as the applications. Numerical examples in finite- and infinite-dimensional spaces illustrate the performances of our scheme.<\/jats:p>","DOI":"10.3390\/axioms12060557","type":"journal-article","created":{"date-parts":[[2023,6,5]],"date-time":"2023-06-05T04:34:51Z","timestamp":1685939691000},"page":"557","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Resolvent-Free Method for Solving Monotone Inclusions"],"prefix":"10.3390","volume":"12","author":[{"given":"Yan","family":"Tang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China"},{"name":"College of Mathematics, Sichuan University, Chengdu 610065, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2150-553X","authenticated-orcid":false,"given":"Aviv","family":"Gibali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Braude College, Karmiel 2161002, Israel"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1215\/S0012-7094-62-02933-2","article-title":"Monotone (nonlinear)operators in Hilbert spaces","volume":"29","author":"Minty","year":"1962","journal-title":"Duke Math. 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