{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:30:37Z","timestamp":1760243437530,"version":"build-2065373602"},"reference-count":7,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,9,13]],"date-time":"2022-09-13T00:00:00Z","timestamp":1663027200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003086","name":"Basque Government","doi-asserted-by":"publisher","award":["1207-19"],"award-info":[{"award-number":["1207-19"]}],"id":[{"id":"10.13039\/501100003086","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In the year 2014, Almeida et al. introduced a new class of mappings, namely, contractions of Geraghty type. Additionally, in the year 2021, Beg et al. introduced the concept of generalized F-proximal contraction of the first kind and generalized F-proximal contraction of the second kind, respectively. After developing these concepts, authors mainly studied the best proximity points for these classes of mappings. In this short note, we prove that the problem of the existence of the best proximity points for the said classes of proximal contractions is equivalent to the corresponding fixed points problems.<\/jats:p>","DOI":"10.3390\/axioms11090468","type":"journal-article","created":{"date-parts":[[2022,9,13]],"date-time":"2022-09-13T21:06:52Z","timestamp":1663103212000},"page":"468","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Equivalence between the Existence of Best Proximity Points and Fixed Points for Some Classes of Proximal Contractions"],"prefix":"10.3390","volume":"11","author":[{"given":"Sumit","family":"Som","sequence":"first","affiliation":[{"name":"Department of Mathematics, School of Basic and Applied Sciences, Adamas University, Barasat 700126, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Moosa","family":"Gabeleh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd 68, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9320-9433","authenticated-orcid":false,"given":"Manuel","family":"De la Sen","sequence":"additional","affiliation":[{"name":"Institute of Research and Development of Processes, University of the Basque Country, 48940 Leioa, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Wardowski, D. (2012). Fixed points of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl., 94.","DOI":"10.1186\/1687-1812-2012-94"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"715","DOI":"10.2298\/FIL1404715C","article-title":"Fixed Point Results for F-contractive mappings of Hardy-Rogers-Type","volume":"28","author":"Cosentino","year":"2014","journal-title":"Filomat"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11784-021-00886-w","article-title":"Best proximity point of generalized F-proximal non-self contractions","volume":"23","author":"Beg","year":"2021","journal-title":"J. Fixed Point Theory Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"957","DOI":"10.1007\/s13398-013-0154-2","article-title":"Existence and uniqueness of best proximity point for contractions of Geraghty type","volume":"108","author":"Almeida","year":"2014","journal-title":"Rev. R. Acad. Cienc. Exactas F\u2019\u0131s Nat. Ser. A Mat. RACSAM"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1007\/s10474-021-01139-5","article-title":"A note on the paper \u201cBest proximity point results for p -proximal contractions\u201d","volume":"164","author":"Gabeleh","year":"2021","journal-title":"Acta Math. Hungarica"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Gabeleh, M., and Markin, J. (2021). Some notes on the paper \u201cOn best proximity points of interpolative proximal contractions\u201d. Quaest. Math., 1\u20136.","DOI":"10.1007\/s10474-021-01139-5"},{"key":"ref_7","first-page":"313","article-title":"Best proximity points for proximal contractions","volume":"15","year":"2014","journal-title":"J. Nonlinear. Convex. Anal."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/9\/468\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:30:39Z","timestamp":1760142639000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/9\/468"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,13]]},"references-count":7,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2022,9]]}},"alternative-id":["axioms11090468"],"URL":"https:\/\/doi.org\/10.3390\/axioms11090468","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2022,9,13]]}}}