{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T10:43:53Z","timestamp":1783421033864,"version":"3.54.6"},"reference-count":31,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T00:00:00Z","timestamp":1762819200000},"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 proposes an efficient iteration method for fixed-point approximation in Banach spaces. The method accelerates convergence by incorporating a squared operator term within the iteration process. Analytical proofs verify its convergence and stability. Comparative numerical tests show that it converges faster and more reliably than established Picard-type methods. Its application to fractional models involving the Gamma function highlights the method\u2019s efficiency and potential for broader use in nonlinear and fractional systems.<\/jats:p>","DOI":"10.3390\/axioms14110830","type":"journal-article","created":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T08:57:41Z","timestamp":1762851461000},"page":"830","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["An Efficient Iteration Method for Fixed-Point Approximation and Its Application to Fractional Volterra\u2013Fredholm Integro\u2013Differential Equations"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3501-8457","authenticated-orcid":false,"given":"Ekta","family":"Sharma","sequence":"first","affiliation":[{"name":"Department of Mathematics, National Institute of Technology Manipur, Langol, Imphal 795004, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-4555-2160","authenticated-orcid":false,"given":"Shubham Kumar","family":"Mittal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National Institute of Technology Manipur, Langol, Imphal 795004, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6860-5220","authenticated-orcid":false,"given":"Sunil","family":"Panday","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National Institute of Technology Manipur, Langol, Imphal 795004, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8524-743X","authenticated-orcid":false,"given":"Lorentz","family":"J\u00e4ntschi","sequence":"additional","affiliation":[{"name":"Department of Physics and Chemistry, Technical University of Cluj-Napoca, B.-dul Muncii nr. 103-105, 400641 Cluj-Napoca, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,11]]},"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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