{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,17]],"date-time":"2025-12-17T18:10:51Z","timestamp":1765995051036,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,9,14]],"date-time":"2022-09-14T00:00:00Z","timestamp":1663113600000},"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 article, we develop a faster iteration method, called the A\u2217\u2217 iteration method, for approximating the fixed points of almost contraction mappings and generalized \u03b1-nonexpansive mappings. We establish some weak and strong convergence results of the A\u2217\u2217 iteration method for fixed points of generalized \u03b1-nonexpansive mappings in uniformly convex Banach spaces. We provide a numerical example to illustrate the efficiency of our new iteration method. The weak w2-stability result of the new iteration method is also studied. As an application of our main results, we approximate the solution of a fractional Volterra\u2013Fredholm integro-differential equation. Our results improve and generalize several well-known results in the current literature.<\/jats:p>","DOI":"10.3390\/axioms11090470","type":"journal-article","created":{"date-parts":[[2022,9,14]],"date-time":"2022-09-14T20:50:45Z","timestamp":1663188645000},"page":"470","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Solving Fractional Volterra\u2013Fredholm Integro-Differential Equations via A** Iteration Method"],"prefix":"10.3390","volume":"11","author":[{"given":"Austine Efut","family":"Ofem","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Uyo, Uyo P.M. Box 1017, Nigeria"},{"name":"Department of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4041, South Africa"}]},{"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, Jeddah P.O. Box 80203, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4410-3269","authenticated-orcid":false,"given":"Oboyi","family":"Joseph","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Calabar, Calabar P.M. Box 1115, Nigeria"}]},{"given":"Mfon Okon","family":"Udo","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Akwa Ibom State University, Ikot Akpaden, Mkpat Enin P.M. Box 1167, Nigeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5228-1073","authenticated-orcid":false,"given":"Umar","family":"Ishtiaq","sequence":"additional","affiliation":[{"name":"Office of Research, Innovation and Commercialization, University of Management and Technology, Lahore 54770, Pakistan"}]},{"given":"Hamed","family":"Al Sulami","sequence":"additional","affiliation":[{"name":"Department of Mathematics, King Abdulaziz University, Jeddah P.O. Box 80203, Saudi Arabia"}]},{"given":"Chukwuka Fernando","family":"Chikwe","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Calabar, Calabar P.M. Box 1115, Nigeria"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1272","DOI":"10.1073\/pnas.53.6.1272","article-title":"Fixed-point theorems for noncompact mappings in Hilbert space","volume":"53","author":"Browder","year":"1965","journal-title":"Proc. Natl. 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