{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:32:42Z","timestamp":1760239962373,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,2,11]],"date-time":"2019-02-11T00:00:00Z","timestamp":1549843200000},"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 introduce the notion of cyclic      ( \u03b1 , \u03b2 )  \u2013   ( \u03c8 , \u03c6 )  s     -rational-type contraction in b-metric spaces, and using this contraction, we prove common fixed point theorems. Our work generalizes many existing results in the literature. In order to highlight the usefulness of our results, applications to functional equations are given.<\/jats:p>","DOI":"10.3390\/sym11020198","type":"journal-article","created":{"date-parts":[[2019,2,12]],"date-time":"2019-02-12T03:18:20Z","timestamp":1549941500000},"page":"198","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Common Fixed Point Theorem via Cyclic (\u03b1,\u03b2)\u2013(\u03c8,\u03c6)S-Contraction with Applications"],"prefix":"10.3390","volume":"11","author":[{"given":"Mian Bahadur","family":"Zada","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Malakand, Chakdara 18800, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3904-8442","authenticated-orcid":false,"given":"Muhammad","family":"Sarwar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Malakand, Chakdara 18800, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3303-0623","authenticated-orcid":false,"given":"Fahd","family":"Jarad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, \u00c7ankaya University, Ankara 06790, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8889-3768","authenticated-orcid":false,"given":"Thabet","family":"Abdeljawad","sequence":"additional","affiliation":[{"name":"Department of Mathematics and General Sciences, Prince Sultan University, P.O. 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