{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T14:09:13Z","timestamp":1770818953738,"version":"3.50.1"},"reference-count":42,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,7,26]],"date-time":"2024-07-26T00:00:00Z","timestamp":1721952000000},"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 the presence of Banach spaces, a novel iterative algorithm is presented in this study using the Chatterjea\u2013Suzuki\u2013C (CSC) condition, and the convergence theorems are established. The efficacy of the proposed algorithm is discussed analytically and numerically. We explain the solution of the Caputo fractional differential problem using our main result and then provide the numerical simulation to validate the results. Moreover, we use MATLAB R (2021a) to compare the obtained numerical results using the new iterative algorithm with some efficient existing algorithms. The work seems to contribute to the current advancement of fixed-point approximation iterative techniques in Banach spaces.<\/jats:p>","DOI":"10.3390\/axioms13080502","type":"journal-article","created":{"date-parts":[[2024,7,26]],"date-time":"2024-07-26T13:04:59Z","timestamp":1721999099000},"page":"502","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Efficiency of a New Iterative Algorithm Using Fixed-Point Approach in the Settings of Uniformly Convex Banach Spaces"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7581-615X","authenticated-orcid":false,"given":"Rekha","family":"Srivastava","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-7085-9109","authenticated-orcid":false,"given":"Wakeel","family":"Ahmed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Sialkot, Sialkot 51310, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6165-8055","authenticated-orcid":false,"given":"Asifa","family":"Tassaddiq","sequence":"additional","affiliation":[{"name":"Department of Computer Science, College of Computer and Information Sciences Majmaah University, Al Majmaah 11952, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nouf","family":"Alotaibi","sequence":"additional","affiliation":[{"name":"Department of Computer Science, College of Computer and Information Sciences Majmaah University, Al Majmaah 11952, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,26]]},"reference":[{"key":"ref_1","first-page":"5583824","article-title":"A Modified Iterative Approach for Fixed Point Problem in Hadamard Spaces","volume":"1","author":"Tassaddiq","year":"2024","journal-title":"J. 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