{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:29:32Z","timestamp":1760228972471,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,5,27]],"date-time":"2022-05-27T00:00:00Z","timestamp":1653609600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The Basque Government","award":["IT1207-19"],"award-info":[{"award-number":["IT1207-19"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The study of symmetry is a major tool in the nonlinear analysis. The symmetricity of distance function in a metric space plays important role in proving the existence of a fixed point for a self mapping. In this work, we approximate a fixed point of noncyclic relatively nonexpansive mappings by using a three-step Thakur iterative scheme in uniformly convex Banach spaces. We also provide a numerical example where the Thakur iterative scheme is faster than some well known iterative schemes such as Picard, Mann, and Ishikawa iteration. Finally, we provide a stronger version of our proposed theorem via von Neumann sequences.<\/jats:p>","DOI":"10.3390\/sym14061107","type":"journal-article","created":{"date-parts":[[2022,5,31]],"date-time":"2022-05-31T02:30:06Z","timestamp":1653964206000},"page":"1107","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Approximating Fixed Points of Relatively Nonexpansive Mappings via Thakur Iteration"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4500-7375","authenticated-orcid":false,"given":"V.","family":"Pragadeeswarar","sequence":"first","affiliation":[{"name":"Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore 641105, Tamil Nadu, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3410-9306","authenticated-orcid":false,"given":"R.","family":"Gopi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Engineering, Presidency University, Bengaluru 560064, Karnataka, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9320-9433","authenticated-orcid":false,"given":"M. De la","family":"Sen","sequence":"additional","affiliation":[{"name":"Institute of Research and Development of Processes IIDP, Campus of Leioa, University of the Basque Country, 48940 Leioa, Bizkaia, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,27]]},"reference":[{"key":"ref_1","first-page":"123","article-title":"Two remarks on the method of succesive approximations","volume":"10","author":"Krasnoselskii","year":"1955","journal-title":"Uspekhi Math. Nauk."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1007\/BF00251595","article-title":"Convergence of approximates to fixed points of nonexpansive nonlinear mappings in Banach spaces","volume":"24","author":"Browder","year":"1967","journal-title":"Arch. Ration. Mech. 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