{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:11:01Z","timestamp":1760235061640,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,7,25]],"date-time":"2021-07-25T00:00:00Z","timestamp":1627171200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003086","name":"Basque Government","doi-asserted-by":"publisher","award":["T1207-19"],"award-info":[{"award-number":["T1207-19"]}],"id":[{"id":"10.13039\/501100003086","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this paper, we provide and study the concept of multi-valued generalized (\u03b1,\u03b2)-nonexpansive mappings, which is the multi-valued version of the recently developed generalized (\u03b1,\u03b2)-nonexpansive mappings. We establish some elementary properties and fixed point existence results for these mappings. Moreover, a multi-valued version of the M-iterative scheme is proposed for approximating fixed points of these mappings in the weak and strong senses. Using an example, we also show that M-iterative scheme converges faster as compared to many other schemes for this class of mappings.<\/jats:p>","DOI":"10.3390\/a14080223","type":"journal-article","created":{"date-parts":[[2021,7,25]],"date-time":"2021-07-25T22:06:21Z","timestamp":1627250781000},"page":"223","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Fixed Point Results on Multi-Valued Generalized (\u03b1,\u03b2)-Nonexpansive Mappings in Banach Spaces"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6991-4287","authenticated-orcid":false,"given":"Kifayat","family":"Ullah","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Lakki Marwat, Lakki Marwat 28420, Khyber Pakhtunkhwa, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad Safi Ullah","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Science and Technology, Bannu 28100, Khyber Pakhtunkhwa, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9320-9433","authenticated-orcid":false,"given":"Manuel","family":"de la Sen","sequence":"additional","affiliation":[{"name":"Institute of Research and Development of Processes, Campus of Leioa (Bizkaia), University of the Basque Country, Barrio Sarriena, P.O. Box 644-Bilbao, 48940 Leioa, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,25]]},"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 integrales","volume":"3","author":"Banach","year":"1922","journal-title":"Fund. Math."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Gorniewicz, L. (1999). Topological Fixed Point Theory of Multivalued Mappings, Kluwer Academic Pub.","DOI":"10.1007\/978-94-015-9195-9"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"282","DOI":"10.2140\/pjm.1969.30.475","article-title":"Multi-valued contraction mappings","volume":"30","author":"Nadler","year":"1969","journal-title":"Pac. J. 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