{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T08:38:37Z","timestamp":1780994317431,"version":"3.54.1"},"reference-count":29,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,8,19]],"date-time":"2024-08-19T00:00:00Z","timestamp":1724025600000},"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>In this manuscript, we initiate a large class of enriched (d,Z)-Z-contractions defined on Banach spaces and prove the existence and uniqueness of the fixed point of these contractions. We also provide an example to support our results and give an existence condition for the uniqueness of the solution to the integral equation. The results provided in the manuscript extend, generalize, and modify the existence results. Our research introduces novel fixed-point results under various contractive conditions. Furthermore, we discuss the iterated function system associated with enriched (d,Z)-Z-contractions in Banach spaces and define the enriched Z-Hutchinson operator. A result regarding the convergence of Krasnoselskii\u2019s iteration method and the uniqueness of the attractor via enriched (d,Z)-Z-contractions is also established. Our discoveries not only confirm but also significantly build upon and broaden several established findings in the current body of literature.<\/jats:p>","DOI":"10.3390\/axioms13080562","type":"journal-article","created":{"date-parts":[[2024,8,19]],"date-time":"2024-08-19T10:11:28Z","timestamp":1724062288000},"page":"562","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Enriched Z-Contractions and Fixed-Point Results with Applications to IFS"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0094-7937","authenticated-orcid":false,"given":"Ibrahim","family":"Alraddadi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-2396-2943","authenticated-orcid":false,"given":"Muhammad","family":"Din","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathum Thani 12120, Thailand"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Umar","family":"Ishtiaq","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohammad","family":"Akram","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ioannis K.","family":"Argyros","sequence":"additional","affiliation":[{"name":"Department of Computing and Mathematical Sciences, Cameron University, Lawton, OK 73505, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1512\/iumj.1981.30.30055","article-title":"Fractals and self similarity","volume":"30","author":"Hutchinson","year":"1981","journal-title":"Indiana Univ. 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