{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T04:08:41Z","timestamp":1771646921258,"version":"3.50.1"},"reference-count":19,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,11]],"date-time":"2023-08-11T00:00:00Z","timestamp":1691712000000},"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>The objective of this research paper is to establish the existence and uniqueness of the best proximity and coincidence with best proximity point results, specifically focusing on Geraghty\u2013Pata\u2013Suzuki-type proximal mappings. To achieve this, we introduce three types of mappings, all within the context of a complete metric space: an \u03b1-\u03b8-Geraghty\u2013Pata\u2013Suzuki-type proximal contraction; an \u03b1-\u03b8-generalized Geraghty\u2013Pata\u2013Suzuki-type proximal contraction; and an \u03b1-\u03b8-modified Geraghty\u2013Pata\u2013Suzuki-type proximal contraction. These new results generalize, extend, and unify various results from the existing literature. Symmetry plays a crucial role in solving nonlinear problems in operator theory, and the variables involved in the metric space are symmetric. Several illustrative examples are provided to showcase the superiority of our results over existing approaches.<\/jats:p>","DOI":"10.3390\/sym15081572","type":"journal-article","created":{"date-parts":[[2023,8,11]],"date-time":"2023-08-11T10:20:16Z","timestamp":1691749216000},"page":"1572","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Geraghty\u2013Pata\u2013Suzuki-Type Proximal Contractions and Related Coincidence Best Proximity Point Results"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1485-6163","authenticated-orcid":false,"given":"Naeem","family":"Saleem","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Management and Technology, Lahore 54782, Pakistan"},{"name":"Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Pretoria, Medunsa 0204, South Africa"}]},{"given":"Maneesha Tur","family":"Raazzia","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Management and Technology, Lahore 54782, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6585-2202","authenticated-orcid":false,"given":"Nawab","family":"Hussain","sequence":"additional","affiliation":[{"name":"Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}]},{"given":"Asim","family":"Asiri","sequence":"additional","affiliation":[{"name":"Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"133","DOI":"10.4064\/fm-3-1-133-181","article-title":"Sur les op\u00e9rations dans les ensembles abstraits et leur application aux \u00e9quations int\u00e9grales","volume":"3","author":"Banach","year":"1922","journal-title":"Fundam. Math."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Debnath, P., Konwar, N., and Radenovic, S. (2021). 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