{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T23:05:22Z","timestamp":1781737522840,"version":"3.54.5"},"reference-count":31,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,1,2]],"date-time":"2022-01-02T00:00:00Z","timestamp":1641081600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The objective of the research article is two-fold. Firstly, we present a fixed point result in the context of triple controlled metric type spaces with a distinctive contractive condition involving the controlled functions. Secondly, we consider an initial value problem associated with a nonlinear Volterra\u2013Fredholm integro-dynamic equation and examine the existence and uniqueness of solutions via fixed point theorem in the setting of complete triple controlled metric type spaces. Furthermore, the theorem is applied to illustrate the existence of a unique solution to an integro-dynamic equation.<\/jats:p>","DOI":"10.3390\/axioms11010019","type":"journal-article","created":{"date-parts":[[2022,1,3]],"date-time":"2022-01-03T22:51:50Z","timestamp":1641250310000},"page":"19","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["New Fixed Point Theorem on Triple Controlled Metric Type Spaces with Applications to Volterra\u2013Fredholm Integro-Dynamic Equations"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2426-0574","authenticated-orcid":false,"given":"Kalpana","family":"Gopalan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, Kalavakkam, Chennai 603 110, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7233-4876","authenticated-orcid":false,"given":"Sumaiya Tasneem","family":"Zubair","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, Kalavakkam, Chennai 603 110, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8889-3768","authenticated-orcid":false,"given":"Thabet","family":"Abdeljawad","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia"},{"name":"Department of Medical Research, China Medical University, Taichung 40402, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,2]]},"reference":[{"key":"ref_1","unstructured":"Hilger, S. (1988). Ein Ma\u03b2kettenkalk\u00fcl mit Anvendung auf Zentrumsmannigfaltigkeiten. [Ph.D. Thesis, Universit\u00e4t at W\u00fcrzburg]."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"535","DOI":"10.7153\/mia-04-48","article-title":"Inequalities on time scales: A survey","volume":"4","author":"Agarwal","year":"2001","journal-title":"Math. 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