{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:52:26Z","timestamp":1760233946994,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,3,9]],"date-time":"2021-03-09T00:00:00Z","timestamp":1615248000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This manuscript aims to study a generalized, set-valued, mixed-ordered, variational inclusion problem involving H(\u00b7,\u00b7)-compression XOR-\u03b1M-non-ordinary difference mapping and relaxed cocoercive mapping in real-ordered Hilbert spaces. The resolvent operator associated with H(\u00b7,\u00b7)-compression XOR-\u03b1M-non-ordinary difference mapping is defined, and some of its characteristics are discussed. We prove existence and uniqueness results for the considered generalized, set-valued, mixed-ordered, variational inclusion problem. Further, we put forward a three-step iterative algorithm using a \u2295 operator, and analyze the convergence of the suggested iterative algorithm under some mild assumptions. Finally, we reconfirm the existence and convergence results by an illustrative numerical example.<\/jats:p>","DOI":"10.3390\/sym13030444","type":"journal-article","created":{"date-parts":[[2021,3,9]],"date-time":"2021-03-09T06:22:32Z","timestamp":1615270952000},"page":"444","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Convergence Analysis of a Three-Step Iterative Algorithm for Generalized Set-Valued Mixed-Ordered Variational Inclusion Problem"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7556-8942","authenticated-orcid":false,"given":"Praveen","family":"Agarwal","sequence":"first","affiliation":[{"name":"Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India"},{"name":"Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman AE 346, United Arab Emirates"},{"name":"International Center for Basic and Applied Sciences, Jaipur 302029, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Doaa","family":"Filali","sequence":"additional","affiliation":[{"name":"Department of Mathematical Science, College of Sciences, Princess Nourah Bint Abdulrahman University, Riyadh 84428, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"Akram","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 170, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3217-8295","authenticated-orcid":false,"given":"M.","family":"Dilshad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,9]]},"reference":[{"key":"ref_1","first-page":"4413","article-title":"Formes bilineaires coercivites sur les ensembles convexes","volume":"258","author":"Stampacchia","year":"1964","journal-title":"Comptes Rendus l\u2019Acad. 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