{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T05:28:49Z","timestamp":1775280529254,"version":"3.50.1"},"reference-count":18,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,9,4]],"date-time":"2022-09-04T00:00:00Z","timestamp":1662249600000},"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>Recently, the fixed-circle problems have been studied with different approaches as an interesting and geometric generalization. In this paper, we present some solutions to an open problem CC: what is (are) the condition(s) to make any circle C\u03d60,\u03c3 as the common fixed circle for two (or more than two) self-mappings? To do this, we modify some known contractions which are used in fixed-point theorems such as the Hardy\u2013Rogers-type contraction, Kannan-type contraction, etc.<\/jats:p>","DOI":"10.3390\/axioms11090454","type":"journal-article","created":{"date-parts":[[2022,9,5]],"date-time":"2022-09-05T20:48:25Z","timestamp":1662410905000},"page":"454","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Some Common Fixed-Circle Results on Metric Spaces"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7986-886X","authenticated-orcid":false,"given":"Nabil","family":"Mlaiki","sequence":"first","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4535-4019","authenticated-orcid":false,"given":"Nihal","family":"Ta\u015f","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Bal\u0131kesir University, 10145 Bal\u0131kesir, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7620-3387","authenticated-orcid":false,"given":"Elif","family":"Kaplan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ondokuz May\u0131s University, 55280 Samsun, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0018-9873","authenticated-orcid":false,"given":"Suhad","family":"Subhi Aiadi","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3378-7797","authenticated-orcid":false,"given":"Asma","family":"Karoui Souayah","sequence":"additional","affiliation":[{"name":"Department of Business Administration, College of Science and Humanities, Shaqra University, Dhurma 11961, Saudi Arabia"},{"name":"Institut Pr\u00e9paratoire aux \u00c9tudes d\u2019Ing\u00e9nieurs de Gafsa, Gafsa University, Gafsa 2112, Tunisia"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,4]]},"reference":[{"key":"ref_1","unstructured":"Mlaiki, N., \u00d6zg\u00fcr, N.Y., and Ta\u015f, N. 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E-Notes"},{"key":"ref_5","first-page":"5525472","article-title":"On unique and nonunique fixed points in metric spaces and application to chemical sciences","volume":"2021","author":"Joshi","year":"2021","journal-title":"J. Funct. Spaces"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1515\/jaa-2021-2057","article-title":"Fixed point to fixed circle and activation function in partial metric space","volume":"28","author":"Tomar","year":"2022","journal-title":"J. Appl. Anal."},{"key":"ref_7","first-page":"6681044","article-title":"On Unique and Nonunique Fixed Points and Fixed Circles in-Metric Space and Application to Cantilever Beam Problem","volume":"2021","author":"Joshi","year":"2021","journal-title":"J. Funct. Spaces"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2794","DOI":"10.3906\/mat-1812-44","article-title":"Fixed-disc results via simulation functions","volume":"43","year":"2019","journal-title":"Turk. J. Math."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Mlaiki, N., Ta\u015f, N., and \u00d6zg\u00fcr, N.Y. (2018). On the fixed-circle problem and Khan type contractions. Axioms, 7.","DOI":"10.3390\/axioms7040080"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1186\/1687-1812-2012-94","article-title":"Fixed points of a new type of contractive mappings in complete metric spaces","volume":"2012","author":"Wardowski","year":"2012","journal-title":"Fixed Point Theory Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1112\/jlms\/s1-37.1.74","article-title":"On fixed and periodic points under contractive mappings","volume":"37","author":"Edelstein","year":"1962","journal-title":"J. Lond. Math. Soc."},{"key":"ref_12","first-page":"141","article-title":"The fixed point method in analysis","volume":"1","author":"Nemytskii","year":"1936","journal-title":"Usp. Mat. 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Natur."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/9\/454\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:23:09Z","timestamp":1760142189000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/9\/454"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,4]]},"references-count":18,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2022,9]]}},"alternative-id":["axioms11090454"],"URL":"https:\/\/doi.org\/10.3390\/axioms11090454","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,4]]}}}