{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T09:41:21Z","timestamp":1775554881280,"version":"3.50.1"},"reference-count":18,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,2,27]],"date-time":"2024-02-27T00:00:00Z","timestamp":1708992000000},"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 article introduces a novel iterative process, denoted as F\u2605, designed for the class of generalized \u03b1-Nonexpensive mappings. The study establishes strong and weak convergence theorems within the context of Banach spaces, supported by carefully chosen assumptions. The convergence results contribute to the theoretical foundation of iterative processes in functional analysis. The presented framework is applied to address nonlinear integral equations, showcasing the versatility and applicability of the proposed F* for the class of generalized iteration process. Additionally, the article includes numerical examples that not only validate the theoretical findings but also provide insights into the practical utility of the developed methodology.<\/jats:p>","DOI":"10.3390\/axioms13030156","type":"journal-article","created":{"date-parts":[[2024,2,27]],"date-time":"2024-02-27T11:52:55Z","timestamp":1709034775000},"page":"156","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Iterative Stability Analysis for Generalized \u03b1-Nonexpensive Mappings with Fixed Points"],"prefix":"10.3390","volume":"13","author":[{"given":"Maryam","family":"Iqbal","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Fatima Jinnah Women University, Rawalpindi 46000, Pakistan"}]},{"given":"Amjad","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematical and Statistics, International Islamic University, Islamabad 44000, Pakistan"},{"name":"Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5188-2830","authenticated-orcid":false,"given":"Hamid Al","family":"Sulami","sequence":"additional","affiliation":[{"name":"Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7742-5993","authenticated-orcid":false,"given":"Aftab","family":"Hussain","sequence":"additional","affiliation":[{"name":"Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"133","DOI":"10.4064\/fm-3-1-133-181","article-title":"Sur les operations dans les ensembles abstraits et leur application aux equations integrals","volume":"3","author":"Banach","year":"1922","journal-title":"Fund. Math."},{"key":"ref_2","first-page":"6994660","article-title":"Iterative approximation of fixed points by using F iteration Process in Banach spaces","volume":"2021","author":"Ahmad","year":"2021","journal-title":"J. Funct. 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