{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:10:53Z","timestamp":1760148653414,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,5,26]],"date-time":"2023-05-26T00:00:00Z","timestamp":1685059200000},"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>In this study, we present a more general class of rational-type contractions in the domain of Hilbert spaces, along with a novel coupled implicit relation. We develop several intriguing results and consequences for the existence of unique coupled fixed points. Further, we investigate a necessary condition that guarantees the well-posedness of a coupled fixed-point problem of self-mappings in Hilbert spaces. Some new observations proposed in this research broaden and extend previously published results in the literature.<\/jats:p>","DOI":"10.3390\/axioms12060523","type":"journal-article","created":{"date-parts":[[2023,5,27]],"date-time":"2023-05-27T16:18:43Z","timestamp":1685204323000},"page":"523","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Well-Posedness Scheme for Coupled Fixed-Point Problems Using Generalized Contractions"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3150-3148","authenticated-orcid":false,"given":"Dur-e-Shehwar","family":"Sagheer","sequence":"first","affiliation":[{"name":"Department of Mathematics, Capital University of Science and Technology, Islamabad 44000, Pakistan"}]},{"given":"Isma","family":"Urooj","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Capital University of Science and Technology, Islamabad 44000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4013-8496","authenticated-orcid":false,"given":"Samina","family":"Batul","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Capital University of Science and Technology, Islamabad 44000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9578-2073","authenticated-orcid":false,"given":"Ahmad","family":"Aloqaily","sequence":"additional","affiliation":[{"name":"School of Computer, Data and Mathematical Sciences, Western Sydney University, Sydney 2150, Australia"},{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7986-886X","authenticated-orcid":false,"given":"Nabil","family":"Mlaiki","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,26]]},"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 leurs applications aux \u00e9quations int\u00e9grals","volume":"3","author":"Banach","year":"1922","journal-title":"Fund. 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