{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:50:04Z","timestamp":1760237404406,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,5,11]],"date-time":"2020-05-11T00:00:00Z","timestamp":1589155200000},"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>We propose two new iterative algorithms for solving K-pseudomonotone variational inequality problems in the framework of real Hilbert spaces. These newly proposed methods are obtained by combining the viscosity approximation algorithm, the Picard Mann algorithm and the inertial subgradient extragradient method. We establish some strong convergence theorems for our newly developed methods under certain restriction. Our results extend and improve several recently announced results. Furthermore, we give several numerical experiments to show that our proposed algorithms performs better in comparison with several existing methods.<\/jats:p>","DOI":"10.3390\/axioms9020051","type":"journal-article","created":{"date-parts":[[2020,5,11]],"date-time":"2020-05-11T12:26:30Z","timestamp":1589199990000},"page":"51","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Inertial Subgradient Extragradient Methods for Solving Variational Inequality Problems and Fixed Point Problems"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6544-6714","authenticated-orcid":false,"given":"Godwin Amechi","family":"Okeke","sequence":"first","affiliation":[{"name":"Department of Mathematics, School of Physical Sciences, Federal University of Technology, Owerri, P.M.B. 1526 Owerri, Imo State, Nigeria"},{"name":"Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mujahid","family":"Abbas","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University, Lahore 54000, Pakistan"},{"name":"Department of Mathematics and Applied Mathematics, University of Pretoria ( Hatfield Campus), Lynnwood Road, Pretoria 0002, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9320-9433","authenticated-orcid":false,"given":"Manuel","family":"de la Sen","sequence":"additional","affiliation":[{"name":"Institute of Research and Development of Processes, University of the Basque Country, Campus of Leioa (Bizkaia), P.O. Box 644-Bilbao, Barrio Sarriena, 48940 Leioa, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,5,11]]},"reference":[{"key":"ref_1","first-page":"4413","article-title":"Formes bilineaires coercitives sur les ensembles convexes","volume":"258","author":"Stampacchia","year":"1964","journal-title":"C. R. Acad. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/BF01350721","article-title":"The fixed point theory of multivalued mapping in topological vector spaces","volume":"177","author":"Browder","year":"1968","journal-title":"Math. Ann."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1007\/s10957-010-9757-3","article-title":"The subgradient extragradient method for solving variational inequalities in Hilbert space","volume":"148","author":"Censor","year":"2011","journal-title":"J. Optim. 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