{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:52:36Z","timestamp":1760057556789,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,10]],"date-time":"2025-02-10T00:00:00Z","timestamp":1739145600000},"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 investigate the \u0394-convergence and strong convergence of a sequence generated by the proximal point method for pseudo-monotone equilibrium problems in Hadamard spaces. First, we show the \u0394-convergence of the generated sequence to a solution of the equilibrium problem. Next, we prove the strong convergence of the generated sequence with some additional conditions imposed on the bifunction. Finally, we prove the strong convergence of the generated sequence, by using Halpern\u2019s regularization method, without any additional condition.<\/jats:p>","DOI":"10.3390\/axioms14020127","type":"journal-article","created":{"date-parts":[[2025,2,10]],"date-time":"2025-02-10T03:39:47Z","timestamp":1739158787000},"page":"127","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Proximal Point Methods for Solving Equilibrium Problems in Hadamard Spaces"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8645-8773","authenticated-orcid":false,"given":"Behzad","family":"Djafari Rouhani","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, University of Texas at El Paso, 500 W. University Avenue, El Paso, TX 79968, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0151-0825","authenticated-orcid":false,"given":"Vahid","family":"Mohebbi","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of Texas at El Paso, 500 W. University Avenue, El Paso, TX 79968, USA"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/BF02192244","article-title":"Generalized monotone bifunctions and equilibrium problems","volume":"90","author":"Bianchi","year":"1996","journal-title":"J. Optim. Theory Appl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1023\/A:1004657817758","article-title":"Equilibrium problems with generalized monotone bifunctions and applications to variational inequalities","volume":"105","author":"Chadli","year":"2000","journal-title":"J. Optim. 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