{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T00:40:01Z","timestamp":1759970401376,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,1,20]],"date-time":"2025-01-20T00:00:00Z","timestamp":1737331200000},"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 research presents a new form of iterative technique for Garcia-Falset mapping that outperforms previous iterative methods for contraction mappings. We illustrate this fact through comparison and present the findings graphically. The research also investigates convergence of the new iteration in uniformly convex Banach space and explores its stability. To further support our findings, we present its working on to a BV problem and to a delay DE. Finally, we propose a design of an implicit neural network that can be considered as an extension of a traditional feed forward network.<\/jats:p>","DOI":"10.3390\/axioms14010071","type":"journal-article","created":{"date-parts":[[2025,1,20]],"date-time":"2025-01-20T12:32:52Z","timestamp":1737376372000},"page":"71","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Four-Step T-Stable Generalized Iterative Technique with Improved Convergence and Various Applications"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3442-3488","authenticated-orcid":false,"given":"Quanita","family":"Kiran","sequence":"first","affiliation":[{"name":"School of Electrical Engineering and Computer Science, National University of Sciences and Technology, Sector H-12, Islamabad 44000, Pakistan"}]},{"given":"Shaista","family":"Begum","sequence":"additional","affiliation":[{"name":"School of Natural Sciences, National University of Sciences and Technology, Sector H-12, Islamabad 44000, Pakistan"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,20]]},"reference":[{"key":"ref_1","first-page":"295","article-title":"Numerical reckoning fixed points for Barinde mappings via a faster iteration process","volume":"33","author":"Alagoz","year":"2008","journal-title":"Facta Univ. 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