{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:15:48Z","timestamp":1760058948721,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,5,15]],"date-time":"2025-05-15T00:00:00Z","timestamp":1747267200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research and Libraries, Princess Nourah bint Abdulrahman University","award":["RPFAP-81-1445"],"award-info":[{"award-number":["RPFAP-81-1445"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Herein, we present two hybrid inertial self-adaptive iterative methods for determining the combined solution of the split variational inclusions and fixed-point problems. Our methods include viscosity approximation, fixed-point iteration, and inertial extrapolation in the initial step of each iteration. We employ two self-adaptive step sizes to compute the iterative sequence, which do not require the pre-calculated norm of a bounded linear operator. We prove strong convergence theorems to approximate the common solution of the split variational inclusions and fixed-point problems. Further, we implement our methods and results to examine split variational inequality and split common fixed-point problems. Finally, we illustrate our methods and compare them with some known methods existing in the literature.<\/jats:p>","DOI":"10.3390\/axioms14050373","type":"journal-article","created":{"date-parts":[[2025,5,15]],"date-time":"2025-05-15T07:46:49Z","timestamp":1747295209000},"page":"373","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Hybrid Inertial Self-Adaptive Iterative Methods for Split Variational Inclusion Problems"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2450-3043","authenticated-orcid":false,"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"}]},{"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"}]},{"given":"Atiaf Farhan Yahya","family":"Alfaifi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia"}]},{"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"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1090\/S0002-9939-1953-0054846-3","article-title":"Mean value methods in iteration","volume":"4","author":"Mann","year":"1953","journal-title":"Am. Math. Soc."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1006\/jmaa.1999.6615","article-title":"Viscosity approximation methods for fixed-points problems","volume":"241","author":"Moudafi","year":"2000","journal-title":"J. Math. Anal. 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