{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T22:33:00Z","timestamp":1774737180807,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,13]],"date-time":"2022-12-13T00:00:00Z","timestamp":1670889600000},"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>In this paper, we prove fixed point theorem via orthogonal Geraghty type \u03b1-admissible contraction map in an orthogonal complete Branciari b-metric spaces context. An example is presented to strengthen our main result. We provided an application to find the existence and uniqueness of a solution to the Volterra integral equation. We have compared the approximate solution and exact solution numerically.<\/jats:p>","DOI":"10.3390\/axioms11120728","type":"journal-article","created":{"date-parts":[[2022,12,14]],"date-time":"2022-12-14T02:54:21Z","timestamp":1670986461000},"page":"728","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Solution to Integral Equation in an O-Complete Branciari b-Metric Spaces"],"prefix":"10.3390","volume":"11","author":[{"given":"Menaha","family":"Dhanraj","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Engineering and Technology, College of Engineering and Technology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur, Kanchipuram 603203, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6346-605X","authenticated-orcid":false,"given":"Arul Joseph","family":"Gnanaprakasam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Engineering and Technology, College of Engineering and Technology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur, Kanchipuram 603203, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4191-3338","authenticated-orcid":false,"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":"https:\/\/orcid.org\/0000-0002-3877-2714","authenticated-orcid":false,"given":"Ozgur","family":"Ege","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ege University, Bornova, Izmir 35100, Turkey"}]},{"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, University of the Basque Country, 48940 Leioa, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,13]]},"reference":[{"key":"ref_1","unstructured":"Bakhtin, I.A. 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