{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,14]],"date-time":"2026-02-14T10:10:21Z","timestamp":1771063821848,"version":"3.50.1"},"reference-count":50,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,1,5]],"date-time":"2024-01-05T00:00:00Z","timestamp":1704412800000},"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>The aim of this paper is to propose an inertial-type AA-viscosity algorithm for approximating the common solutions of the split variational inclusion problem, the generalized equilibrium problem and the common fixed-point problem of nonexpansive mappings. The strong convergence of an iterative sequence obtained through the proposed method is proved under some mild assumptions. Consequently, approximations of the solution of the split feasibility problem, the relaxed split feasibility problem, the split common null point problem and the split minimization problem are given. The applicability of our proposed algorithm has been illustrated with the help of a numerical example. Our iterative method was then compared graphically with different comparable methods in the existing literature.<\/jats:p>","DOI":"10.3390\/axioms13010038","type":"journal-article","created":{"date-parts":[[2024,1,5]],"date-time":"2024-01-05T10:06:43Z","timestamp":1704449203000},"page":"38","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["The AA-Viscosity Algorithm for Fixed-Point, Generalized Equilibrium and Variational Inclusion Problems"],"prefix":"10.3390","volume":"13","author":[{"given":"Muhammad Waseem","family":"Asghar","sequence":"first","affiliation":[{"name":"Department of Mathematics, Government College University, Katchery Road, Lahore 54000, Pakistan"}]},{"given":"Mujahid","family":"Abbas","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University, Katchery Road, Lahore 54000, Pakistan"},{"name":"Department of Medical Research, China Medical University, Taichung 404, Taiwan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8645-8773","authenticated-orcid":false,"given":"Behzad Djafari","family":"Rouhani","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, USA"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1137\/S0036144593251710","article-title":"On projection algorithms for solving convex feasibility problems","volume":"38","author":"Bauschke","year":"1996","journal-title":"SIAM Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"025011","DOI":"10.1088\/0266-5611\/29\/2\/025011","article-title":"A primal\u2013dual fixed point algorithm for convex separable minimization with applications to image restoration","volume":"29","author":"Chen","year":"2013","journal-title":"Inverse Probl."},{"key":"ref_3","unstructured":"Goebel, K., and Reich, S. 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