{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T19:22:22Z","timestamp":1769196142565,"version":"3.49.0"},"reference-count":49,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,1]],"date-time":"2023-03-01T00:00:00Z","timestamp":1677628800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Israel Science Foundation","award":["Grant 820\/17"],"award-info":[{"award-number":["Grant 820\/17"]}]},{"name":"Fund for the Promotion of Research at the Technion","award":["Grant 820\/17"],"award-info":[{"award-number":["Grant 820\/17"]}]},{"name":"Technion General Research Fund","award":["Grant 820\/17"],"award-info":[{"award-number":["Grant 820\/17"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this work, we are concerned with the iterative approximation of solutions to equilibrium problems in the framework of Hadamard manifolds. We introduce a subgradient extragradient type method with a self-adaptive step size. The use of a step size which is allowed to increase per iteration is to avoid the dependence of our method on the Lipschitz constant of the underlying operator as has been the case in recent articles in this direction. In general, operators satisfying weak monotonicity conditions seem to be more applicable in practice. By using inertial and viscosity techniques, we establish a convergence result for solving a pseudomonotone equilibrium problem under some appropriate conditions. As applications, we use our method to solve some theoretical optimization problems. Finally, we present some numerical illustrations in order to demonstrate the quantitative efficacy and superiority of our proposed method over a previous method present in the literature.<\/jats:p>","DOI":"10.3390\/axioms12030256","type":"journal-article","created":{"date-parts":[[2023,3,2]],"date-time":"2023-03-02T02:10:59Z","timestamp":1677723059000},"page":"256","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["An Inertial Subgradient Extragradient Method for Approximating Solutions to Equilibrium Problems in Hadamard Manifolds"],"prefix":"10.3390","volume":"12","author":[{"given":"Olawale Kazeem","family":"Oyewole","sequence":"first","affiliation":[{"name":"Department of Mathematics, The Technion\u2014Israel Institute of Technology, Haifa 32000, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0780-1559","authenticated-orcid":false,"given":"Simeon","family":"Reich","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Technion\u2014Israel Institute of Technology, Haifa 32000, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,1]]},"reference":[{"key":"ref_1","first-page":"103","article-title":"A Minimax Inequality and Its Application","volume":"Volume 3","author":"Shisha","year":"1972","journal-title":"Inequalities"},{"key":"ref_2","first-page":"123","article-title":"From optimization and variational inequalities to equilibrium problems","volume":"63","author":"Blum","year":"1994","journal-title":"Math. 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