{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T22:19:47Z","timestamp":1768342787433,"version":"3.49.0"},"reference-count":43,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,11,6]],"date-time":"2023-11-06T00:00:00Z","timestamp":1699228800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Department of Mathematics at the Technion\u2014Israel Institute of Technology","award":["No. 820\/17"],"award-info":[{"award-number":["No. 820\/17"]}]},{"name":"Department of Mathematics at the Technion\u2014Israel Institute of Technology","award":["2001893"],"award-info":[{"award-number":["2001893"]}]},{"name":"Department of Mathematics at the Technion\u2014Israel Institute of Technology","award":["2016723"],"award-info":[{"award-number":["2016723"]}]},{"name":"Israel Science Foundation","award":["No. 820\/17"],"award-info":[{"award-number":["No. 820\/17"]}]},{"name":"Israel Science Foundation","award":["2001893"],"award-info":[{"award-number":["2001893"]}]},{"name":"Israel Science Foundation","award":["2016723"],"award-info":[{"award-number":["2016723"]}]},{"name":"Promotion of Research at the Technion","award":["No. 820\/17"],"award-info":[{"award-number":["No. 820\/17"]}]},{"name":"Promotion of Research at the Technion","award":["2001893"],"award-info":[{"award-number":["2001893"]}]},{"name":"Promotion of Research at the Technion","award":["2016723"],"award-info":[{"award-number":["2016723"]}]},{"name":"Technion General Research Fund","award":["No. 820\/17"],"award-info":[{"award-number":["No. 820\/17"]}]},{"name":"Technion General Research Fund","award":["2001893"],"award-info":[{"award-number":["2001893"]}]},{"name":"Technion General Research Fund","award":["2016723"],"award-info":[{"award-number":["2016723"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We study three classes of variational inclusion problems in the framework of a real Hilbert space and propose a simple modification of Tseng\u2019s forward-backward-forward splitting method for solving such problems. Our algorithm is obtained via a certain regularization procedure and uses self-adaptive step sizes. We show that the approximating sequences generated by our algorithm converge strongly to a solution of the problems under suitable assumptions on the regularization parameters. Furthermore, we apply our results to an elastic net penalty problem in statistical learning theory and to split feasibility problems. Moreover, we illustrate the usefulness and effectiveness of our algorithm by using numerical examples in comparison with some existing relevant algorithms that can be found in the literature.<\/jats:p>","DOI":"10.3390\/axioms12111037","type":"journal-article","created":{"date-parts":[[2023,11,6]],"date-time":"2023-11-06T08:15:56Z","timestamp":1699258556000},"page":"1037","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Regularized Tseng Method for Solving Various Variational Inclusion Problems and Its Application to a Statistical Learning Model"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5939-935X","authenticated-orcid":false,"given":"Adeolu","family":"Taiwo","sequence":"first","affiliation":[{"name":"Department of Mathematics, The Technion\u2014Israel Institute of Technology, 3200003 Haifa, Israel"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0780-1559","authenticated-orcid":false,"given":"Simeon","family":"Reich","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Technion\u2014Israel Institute of Technology, 3200003 Haifa, Israel"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,6]]},"reference":[{"key":"ref_1","unstructured":"Alber, Y., and Ryazantseva, I. 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