{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:18:08Z","timestamp":1760059088589,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,5,23]],"date-time":"2025-05-23T00:00:00Z","timestamp":1747958400000},"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>Let nonempty subsets E and F of a Banach space X be given, along with a mapping S:E\u222aF\u2192E\u222aF defined as noncyclic when S(E)\u2286E and S(F)\u2286F. In this case, an optimal pair of fixed points is defined as a point (p,q)\u2208E\u00d7F where p and q are fixed points of S that estimate the distance between E and F. This article explores an extended version of G\u00f6hde\u2019s fixed point problem to identify optimal fixed point pairs for noncyclic relatively nonexpansive maps in strictly convex Banach spaces, while introducing new classes of noncyclic Kannan contractions, noncyclic relatively Kannan nonexpansive contractions using the proximal projection mapping defined on union of proximal pairs, and proving additional existence results with supporting examples.<\/jats:p>","DOI":"10.3390\/axioms14060400","type":"journal-article","created":{"date-parts":[[2025,5,23]],"date-time":"2025-05-23T12:24:18Z","timestamp":1748003058000},"page":"400","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Extensions of G\u00f6hde and Kannan Fixed Point Theorems in Strictly Convex Banach Spaces"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5439-1631","authenticated-orcid":false,"given":"Moosa","family":"Gabeleh","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Basic Sciences, Ayatollah Boroujerdi University, Boroujerd 6919969737, Iran"},{"name":"Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Pretoria 0204, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9640-7846","authenticated-orcid":false,"given":"Maggie","family":"Aphane","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Pretoria 0204, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,23]]},"reference":[{"key":"ref_1","first-page":"837","article-title":"On the center of a convex set","volume":"USSR 59","author":"Brodskii","year":"1948","journal-title":"Dokl. 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