{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T00:54:25Z","timestamp":1773017665880,"version":"3.50.1"},"reference-count":26,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,14]],"date-time":"2025-02-14T00:00:00Z","timestamp":1739491200000},"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>This paper aims to establish several fixed-point theorems within the framework of Banach spaces endowed with a binary relation. By utilizing enriched contraction principles involving two classes of altering-distance functions, the study encompasses various types of contractive mappings, including theoretic-order contractions, Picard\u2013Banach contractions, weak contractions, and non-expansive contractions. A suitable Krasnoselskij iterative scheme is employed to derive the results. Many well-known fixed-point theorems (FPTs) can be obtained as special cases of these findings by assigning specific control functions in the main definitions or selecting an appropriate binary relation. To validate the theoretical results, numerous illustrative examples are provided. Furthermore, the paper demonstrates the applicability of the findings through applications to ordinary differential equations.<\/jats:p>","DOI":"10.3390\/axioms14020135","type":"journal-article","created":{"date-parts":[[2025,2,14]],"date-time":"2025-02-14T11:14:41Z","timestamp":1739531681000},"page":"135","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Certain Fixed-Point Results for (e,\u03c8,\u03a6)-Enriched Weak Contractions via Theoretic Order with Applications"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5228-1073","authenticated-orcid":false,"given":"Umar","family":"Ishtiaq","sequence":"first","affiliation":[{"name":"Office of Research, Innovation and Commecialization, University of Management and Technology, Lahore 54770, Pakistan"}]},{"given":"Muhammad","family":"Din","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Khlong Luang 12120, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1859-4332","authenticated-orcid":false,"given":"Yumnam","family":"Rohen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Manipur University, Imphal 795003, India"}]},{"given":"Khalid A.","family":"Alnowibet","sequence":"additional","affiliation":[{"name":"Statistics and Operations Research Department, College of Science, King Saud University, Riyadh 11451, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8042-1806","authenticated-orcid":false,"given":"Ioan-Lucian","family":"Popa","sequence":"additional","affiliation":[{"name":"Department of Computing, Mathematics and Electronics, \u201c1 Decembrie 1918\u201d University of Alba Iulia, 510009 Alba Iulia, Romania"},{"name":"Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, 500091 Brasov, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"133","DOI":"10.4064\/fm-3-1-133-181","article-title":"Sur les op\u00e9rations dans les ensembles abstraits et leur application aux \u00e9quations int\u00e9grales","volume":"3","author":"Banach","year":"1922","journal-title":"Fundam. 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