{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:56:21Z","timestamp":1760237781293,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,7,21]],"date-time":"2022-07-21T00:00:00Z","timestamp":1658361600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research at Princess Nourah bint Abdulrahman University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The goal of this paper is to propose and investigate new iterative methods for examining an approximate solution of a fixed-point problem, an equilibrium problem, and a finite collection of variational inclusions in the Hadamard manifold\u2019s structure. Operating under some assumptions, we extend the proximal point algorithm to estimate the common solution of stated problems and obtain a strong convergence theorem for the common solution. We also present several consequences of the proposed iterative methods and their convergence results.<\/jats:p>","DOI":"10.3390\/axioms11070352","type":"journal-article","created":{"date-parts":[[2022,7,21]],"date-time":"2022-07-21T10:36:56Z","timestamp":1658399816000},"page":"352","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Iterative Approximate Solutions for Variational Problems in Hadamard Manifold"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3217-8295","authenticated-orcid":false,"given":"Mohammad","family":"Dilshad","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia"}]},{"given":"Doaa","family":"Filali","sequence":"additional","affiliation":[{"name":"Department of Mathematical Science, College of Sciences, Princess Nourah Bint Abdulrahman University, Riyadh 84428, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1928-2952","authenticated-orcid":false,"given":"Sumit","family":"Chandok","sequence":"additional","affiliation":[{"name":"School of Mathematics, Thapar Institute of Engineering & Technology, Patiala 147004, Punjab, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1416-5351","authenticated-orcid":false,"given":"Mohammad","family":"Akram","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Islamic University of Madinah, P.O. 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