{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T12:42:15Z","timestamp":1771677735319,"version":"3.50.1"},"reference-count":21,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,3,11]],"date-time":"2021-03-11T00:00:00Z","timestamp":1615420800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Basque Government","award":["IT1207-19"],"award-info":[{"award-number":["IT1207-19"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The main result of this paper is a fixed-point theorem for multivalued contractions obtained through an inequality with rational terms. The contraction is an F-type contraction. The results are obtained in a metric space endowed with a graph. The main theorem is supported by illustrative examples. Several results as special cases are obtained by specific choices of the control functions involved in the inequality. The study is broadly in the domain of setvalued analysis. The methodology of the paper is a blending of both graph theoretic and analytic methods.<\/jats:p>","DOI":"10.3390\/axioms10010031","type":"journal-article","created":{"date-parts":[[2021,3,11]],"date-time":"2021-03-11T20:17:40Z","timestamp":1615493860000},"page":"31","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Fixed-Point Study of Generalized Rational Type Multivalued Contractive Mappings on Metric Spaces with a Graph"],"prefix":"10.3390","volume":"10","author":[{"given":"Binayak","family":"Choudhury","sequence":"first","affiliation":[{"name":"Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, West Bengal, India"}]},{"given":"Nikhilesh","family":"Metiya","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sovarani Memorial College, Jagatballavpur, Howrah 711408, West Bengal, India"}]},{"given":"Debashis","family":"Khatua","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, West Bengal, India"}]},{"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, Faculty of Science and Technology, Campus of Leioa, University of the Basque Country, Bizkaia, 48940 Leioa, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"475","DOI":"10.2140\/pjm.1969.30.475","article-title":"Multi-valued contraction mappings","volume":"30","author":"Nadler","year":"1969","journal-title":"Pac. 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On F-contractions for weak \u03b1-admissible mappings in metric-like spaces. Mathematics, 8.","DOI":"10.3390\/math8091629"},{"key":"ref_12","first-page":"146","article-title":"Fixed points of F-weak contractions on complete metric spaces","volume":"XLVII","author":"Wardowski","year":"2014","journal-title":"Demonstr. 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