{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T04:58:53Z","timestamp":1776229133562,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,1,24]],"date-time":"2025-01-24T00:00:00Z","timestamp":1737676800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002383","name":"King Saud University","doi-asserted-by":"publisher","award":["RSPD2025R687"],"award-info":[{"award-number":["RSPD2025R687"]}],"id":[{"id":"10.13039\/501100002383","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this manuscript, we present several novel results in fixed-point theory for a complete controlled metric space. The first presented result is inspired from the Caristi contraction where we explore the existence and uniqueness of fixed points under specific conditions. Furthermore, we propose a graphical form of it by endowing the considered space with a graph and develop a new fixed-point theorem, which is illustrated by two examples. Also, we establish a theorem for the \u03b1-admissible mapping. To demonstrate its effectiveness, the last theorem proposes an approach to solve a second-order differential equation.<\/jats:p>","DOI":"10.3390\/axioms14020085","type":"journal-article","created":{"date-parts":[[2025,1,24]],"date-time":"2025-01-24T03:26:31Z","timestamp":1737689191000},"page":"85","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["New Fixed-Point Results in Controlled Metric Type Spaces with Applications"],"prefix":"10.3390","volume":"14","author":[{"given":"Nizar","family":"Souayah","sequence":"first","affiliation":[{"name":"Department of Natural Sciences, Community College Al-Riyadh, King Saud University, Riyadh 11421, Saudi Arabia"}]},{"given":"Lotfi","family":"Hidri","sequence":"additional","affiliation":[{"name":"Industrial Engineering Department, College of Engineering, King Saud University, Riyadh 11421, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"133181","DOI":"10.4064\/fm-3-1-133-181","article-title":"Sur les operations dans les ensembles abstraits et leur applications aux equations integrales","volume":"3","author":"Banach","year":"1922","journal-title":"Fundam. 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