{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T22:19:04Z","timestamp":1775168344779,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,4,7]],"date-time":"2021-04-07T00:00:00Z","timestamp":1617753600000},"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 paper, we establish the existence of fixed points of rational type contractions in the setting of extended b-metric spaces. Our results extend considerably several well-known results in the existing literature. We present some nontrivial examples to show the validity of our results. Furthermore, as applications, we obtain the existence of solution to a class of Fredholm integral equations.<\/jats:p>","DOI":"10.3390\/sym13040614","type":"journal-article","created":{"date-parts":[[2021,4,7]],"date-time":"2021-04-07T03:52:03Z","timestamp":1617767523000},"page":"614","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Rational Type Contractions in Extended b-Metric Spaces"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1836-2873","authenticated-orcid":false,"given":"Huaping","family":"Huang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404020, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8339-0731","authenticated-orcid":false,"given":"Yumnam Mahendra","family":"Singh","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences and Humanities, Manipur Institute of Technology, A Constituent College of Manipur University, Takelpat 795004, Manipur, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0216-241X","authenticated-orcid":false,"given":"Mohammad Saeed","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa 0208, South Africa"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8254-6688","authenticated-orcid":false,"given":"Stojan","family":"Radenovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,7]]},"reference":[{"key":"ref_1","first-page":"26","article-title":"The contraction mapping principle in almost metric spaces","volume":"30","author":"Bakhtin","year":"1989","journal-title":"Funct. 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