{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T15:27:40Z","timestamp":1767108460938,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,8,30]],"date-time":"2023-08-30T00:00:00Z","timestamp":1693353600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper aims to present two inertial iterative algorithms for estimating the solution of split variational inclusion (SpVIsP) and its extended version for estimating the common solution of (SpVIsP) and fixed point problem (FPP) of a nonexpansive mapping in the setting of real Hilbert spaces. We establish the weak convergence of the proposed algorithms and strong convergence of the extended version without using the pre-estimated norm of a bounded linear operator. We also exhibit the reliability and behavior of the proposed algorithms using appropriate assumptions in a numerical example.<\/jats:p>","DOI":"10.3390\/axioms12090848","type":"journal-article","created":{"date-parts":[[2023,8,30]],"date-time":"2023-08-30T10:30:52Z","timestamp":1693391452000},"page":"848","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Inertial Iterative Algorithms for Split Variational Inclusion and Fixed Point Problems"],"prefix":"10.3390","volume":"12","author":[{"given":"Doaa","family":"Filali","sequence":"first","affiliation":[{"name":"Department of Mathematical Science, College of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3217-8295","authenticated-orcid":false,"given":"Mohammad","family":"Dilshad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lujain Saud Muaydhid","family":"Alyasi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1416-5351","authenticated-orcid":false,"given":"Mohammad","family":"Akram","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Islamic University of Madinah, P.O. Box 170, Madinah 42351, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/BF02142692","article-title":"A multi projection algorithm using Bregman projections in a product space","volume":"8","author":"Censor","year":"1994","journal-title":"Numer. Algor."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2353","DOI":"10.1088\/0031-9155\/51\/10\/001","article-title":"A unified approach for inversion problem in intensity modulated radiation therapy","volume":"51","author":"Censor","year":"2006","journal-title":"Phys. Med. 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