{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T07:55:51Z","timestamp":1780473351914,"version":"3.54.1"},"reference-count":28,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,7,3]],"date-time":"2020-07-03T00:00:00Z","timestamp":1593734400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>We introduce a very general class of generalized non-expansive maps. This new class of maps properly includes the class of Suzuki non-expansive maps, Reich\u2013Suzuki type non-expansive maps, and generalized    \u03b1   -non-expansive maps. We establish some basic properties and demiclosed principle for this class of maps. After this, we establish existence and convergence results for this class of maps in the context of uniformly convex Banach spaces and compare several well known iterative algorithms.<\/jats:p>","DOI":"10.3390\/computation8030061","type":"journal-article","created":{"date-parts":[[2020,7,3]],"date-time":"2020-07-03T06:51:20Z","timestamp":1593759080000},"page":"61","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["On Generalized Nonexpansive Maps in Banach Spaces"],"prefix":"10.3390","volume":"8","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 Science and Technology, Bannu 28100, Khyber Pakhtunkhwa, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8119-9546","authenticated-orcid":false,"given":"Junaid","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Science and Technology, Bannu 28100, Khyber Pakhtunkhwa, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9320-9433","authenticated-orcid":false,"given":"Manuel de la","family":"Sen","sequence":"additional","affiliation":[{"name":"Institute of Research and Development of Processes, University of the Basque Country, Campus of Leioa (Bizkaia), P.O. Box 644- Bilbao, Barrio Sarriena, 48940 Leioa, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1004","DOI":"10.2307\/2313345","article-title":"A fixed point theorem for mappings which do not increase distance","volume":"72","author":"Kirk","year":"1965","journal-title":"Am. Math. Mon."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1041","DOI":"10.1073\/pnas.54.4.1041","article-title":"Nonexpansive nonlinear operators in a Banach space","volume":"54","author":"Browder","year":"1965","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1002\/mana.19650300312","article-title":"Zum Prinzip der Kontraktiven Abbildung","volume":"30","author":"Gohde","year":"1965","journal-title":"Math. 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