{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,28]],"date-time":"2026-05-28T00:20:00Z","timestamp":1779927600834,"version":"3.53.1"},"reference-count":37,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,2,24]],"date-time":"2019-02-24T00:00:00Z","timestamp":1550966400000},"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>In this manuscript, we present some results related to fixed-discs of self-mappings in rectangular metric spaces. To do this, we give new techniques modifying some classical notions such as Banach contraction principle, \u03b1-admissible mappings and Brianciari type contractions. We give necessary illustrative examples to show the validity of our obtained theoretical theorems. Our results are generalizations of some fixed-circle results existing in the literature.<\/jats:p>","DOI":"10.3390\/sym11020294","type":"journal-article","created":{"date-parts":[[2019,2,25]],"date-time":"2019-02-25T03:06:52Z","timestamp":1551064012000},"page":"294","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Fixed-Discs in Rectangular Metric Spaces"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3896-3809","authenticated-orcid":false,"given":"Hassen","family":"Aydi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Imam Abdulrahman Bin Faisal University, College of Education in Jubail, P.O. Box 12020, Industrial Jubail 31961, Saudi Arabia"},{"name":"China Medical University Hospital, China Medical University, Taichung 40402, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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, Bal\u0131kesir 10145, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8152-1830","authenticated-orcid":false,"given":"Nihal Y\u0131lmaz","family":"\u00d6zg\u00fcr","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Bal\u0131kesir University, Bal\u0131kesir 10145, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nabil","family":"Mlaiki","sequence":"additional","affiliation":[{"name":"Department of Mathematics and General Sciences, Prince Sultan University, P. O. Box 66833, Riyadh 11586, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1109\/TNN.2008.2005605","article-title":"The graph neural network model","volume":"20","author":"Scarselli","year":"2009","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_2","unstructured":"Mandic, D.P. (2000, January 11\u201313). The use of M\u00f6bius transformations in neural networks and signal processing. Proceedings of the Neural Networks for Signal Processing X, Sydney, NSW, Australia."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4698","DOI":"10.1016\/j.cnsns.2011.03.005","article-title":"Complex valued neural network with M\u00f6bius activation function, Commun","volume":"16","year":"2011","journal-title":"Nonlinear Sci. Numer. 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