{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:04:41Z","timestamp":1760148281978,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,15]],"date-time":"2023-04-15T00:00:00Z","timestamp":1681516800000},"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 article, we introduce the concept of weak F\u211cm,\u03b7-contractions on relation-theoretic m-metric spaces and establish related fixed point theorems, where \u03b7 is a control function and \u211c is a relation. Then, we detail some fixed point results for cyclic-type weak F\u211cm,\u03b7-contraction mappings. Finally, we demonstrate some illustrative examples and discuss upper and lower solutions of Volterra-type integral equations of the form \u03be\u03b1=\u222b0\u03b1A\u03b1,\u03c3,\u03be\u03c3m\u03c3+\u03a8\u03b1,\u03b1\u22080,1.<\/jats:p>","DOI":"10.3390\/sym15040922","type":"journal-article","created":{"date-parts":[[2023,4,17]],"date-time":"2023-04-17T03:14:09Z","timestamp":1681701249000},"page":"922","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On Relational Weak F\u211cm,\u03b7-Contractive Mappings and Their Applications"],"prefix":"10.3390","volume":"15","author":[{"given":"Muhammad","family":"Tariq","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3041-328X","authenticated-orcid":false,"given":"Muhammad","family":"Arshad","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan"}]},{"given":"Eskandar","family":"Ameer","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Taiz University, Taiz 6803, Yemen"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9578-2073","authenticated-orcid":false,"given":"Ahmad","family":"Aloqaily","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia"},{"name":"School of Computer, Data and Mathematical Sciences, Western Sydney University, Sydney 2150, Australia"}]},{"given":"Suhad Subhi","family":"Aiadi","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 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, P.O. Box 66833, Riyadh 11586, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"133","DOI":"10.4064\/fm-3-1-133-181","article-title":"Sur les operations dans les ensembles abstraits et leurs applications aux equations integrales","volume":"3","author":"Banach","year":"1922","journal-title":"Fund. 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