{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,9]],"date-time":"2023-10-09T12:24:41Z","timestamp":1696854281428},"reference-count":26,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,22]],"date-time":"2023-03-22T00:00:00Z","timestamp":1679443200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Prince Sattam Bin Abdulaziz University","award":["PSAU\/2023\/R\/1444"]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"In this article, we establish fixed point results by defining the concept of F-Khan contraction of an orthogonal set by modifying the symmetry of usual contractive conditions. We also provide illustrative examples to support our results. The derived results have been applied to find analytical solutions to integral equations. The analytical solutions are verified with numerical simulation.<\/jats:p>","DOI":"10.3390\/sym15030773","type":"journal-article","created":{"date-parts":[[2023,3,22]],"date-time":"2023-03-22T11:46:43Z","timestamp":1679485603000},"page":"773","source":"Crossref","is-referenced-by-count":1,"title":["Application of Fixed-Point Results to Integral Equation through F-Khan Contraction"],"prefix":"10.3390","volume":"15","author":[{"given":"Arul Joseph","family":"Gnanaprakasam","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, India"}]},{"given":"Gunaseelan","family":"Mani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602105, India"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-9027-0810","authenticated-orcid":false,"given":"Rajagopalan","family":"Ramaswamy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia"}]},{"given":"Ola A. Ashour","family":"Abdelnaby","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia"},{"name":"Department of Mathematics, Cairo University, Cairo 12613, Egypt"}]},{"given":"Khizar Hyatt","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia"}]},{"given":"Stojan","family":"Radenovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF03018603","article-title":"Sur quelques points du calcul fonctionnel","volume":"22","year":"1906","journal-title":"Rend. 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On the fixed-circle problem and Khan type contractions. Axioms, 7.","DOI":"10.3390\/axioms7040080"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/3\/773\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,22]],"date-time":"2023-03-22T12:54:50Z","timestamp":1679489690000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/3\/773"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,22]]},"references-count":26,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,3]]}},"alternative-id":["sym15030773"],"URL":"https:\/\/doi.org\/10.3390\/sym15030773","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,3,22]]}}}
