{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:36:44Z","timestamp":1760240204339,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,4,3]],"date-time":"2019-04-03T00:00:00Z","timestamp":1554249600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper presents two shrinking extragradient algorithms that can both find the solution sets of equilibrium problems for pseudomonotone bifunctions and find the sets of fixed points of quasi-nonexpansive mappings in a real Hilbert space. Under some constraint qualifications of the scalar sequences, these two new algorithms show strong convergence. Some numerical experiments are presented to demonstrate the new algorithms. Finally, the two introduced algorithms are compared with a standard, well-known algorithm.<\/jats:p>","DOI":"10.3390\/sym11040480","type":"journal-article","created":{"date-parts":[[2019,4,4]],"date-time":"2019-04-04T03:13:42Z","timestamp":1554347622000},"page":"480","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Shrinking Extragradient Method for Pseudomonotone Equilibrium Problems and Quasi-Nonexpansive Mappings"],"prefix":"10.3390","volume":"11","author":[{"given":"Manatchanok","family":"Khonchaliew","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand"}]},{"given":"Ali","family":"Farajzadeh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Razi University, Kermanshah 67149, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6539-7107","authenticated-orcid":false,"given":"Narin","family":"Petrot","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand"},{"name":"Centre of Excellence in Nonlinear Analysis and Optimization, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,3]]},"reference":[{"key":"ref_1","first-page":"127","article-title":"From optimization and variational inequalities to equilibrium problems","volume":"63","author":"Blum","year":"1994","journal-title":"Math. 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