{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T04:37:21Z","timestamp":1787027841445,"version":"3.56.0"},"reference-count":8,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2025,12,1]],"date-time":"2025-12-01T00:00:00Z","timestamp":1764547200000},"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>In 2003 W. Takahashi and M. Toyoda showed the weak convergence of an iteration process of finding the solution of a variational inequality problem for an inverse strongly monotone mapping. In the present paper, we show that for the same process, most of its iterates are approximate common solutions for a finite family of variational inequalities induced by inverse strongly monotone mappings.<\/jats:p>","DOI":"10.3390\/axioms14120893","type":"journal-article","created":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T16:41:41Z","timestamp":1765212101000},"page":"893","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Approximate Common Solutions for a Family of Inverse Strongly Monotone Mappings"],"prefix":"10.3390","volume":"14","author":[{"given":"Alexander J.","family":"Zaslavski","sequence":"first","affiliation":[{"name":"Department of Mathematics, The Technion\u2014Israel Institute of Technology, Haifa 32000, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1023\/A:1025407607560","article-title":"Weak convergence theorems for nonexpansive mappings and monotone mappings","volume":"118","author":"Takahashi","year":"2003","journal-title":"J. Optim. Theory Appl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/0022-247X(67)90085-6","article-title":"Construction of fixed Points of nonlinear mappings in Hilbert space","volume":"20","author":"Browder","year":"1967","journal-title":"J. Math. Anal. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1023\/A:1008643727926","article-title":"Regularization of nonlinear ill-posed variational inequalities and convergence rates","volume":"6","author":"Liu","year":"1998","journal-title":"Set-Val. Anal."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Bauschke, H.H., and Combettes, P.L. (2011). Convex Analysis and Monotone Operator Theory in Hilbert Spaces, Springer.","DOI":"10.1007\/978-1-4419-9467-7"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Deutsch, F. (2001). Best approximation in inner product spaces. CMS Books in Mathematics\/Ouvrages de Mathmatiques de la SMC, Springer.","DOI":"10.1007\/978-1-4684-9298-9"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Zaslavski, A.J. (2016). Numerical Optimization with Computational Errors, Springer. Springer Optimization and Its Applications.","DOI":"10.1007\/978-3-319-30921-7"},{"key":"ref_7","first-page":"326","article-title":"Calcolo approssimato per le soluzioni dei sistemi di equazioni lineari","volume":"1","author":"Cimmino","year":"1938","journal-title":"Ric. Sci."},{"key":"ref_8","unstructured":"Censor, Y., and Zenios, S. (1997). Parallel Optimization: Theory, Algorithms and Applications, Oxford University Press."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/12\/893\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T16:44:28Z","timestamp":1765212268000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/12\/893"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,1]]},"references-count":8,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["axioms14120893"],"URL":"https:\/\/doi.org\/10.3390\/axioms14120893","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,1]]}}}