{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:11:21Z","timestamp":1760058681490,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,16]],"date-time":"2025-04-16T00:00:00Z","timestamp":1744761600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Scientific Research Foundation of Harbin Cambridge University","award":["2024JQKY2","NJZY22215","2024MS01005"],"award-info":[{"award-number":["2024JQKY2","NJZY22215","2024MS01005"]}]},{"name":"Science Research Project of Inner Mongolia Autonomous Region","award":["2024JQKY2","NJZY22215","2024MS01005"],"award-info":[{"award-number":["2024JQKY2","NJZY22215","2024MS01005"]}]},{"name":"Natural Science Foundation of Inner Mongolia","award":["2024JQKY2","NJZY22215","2024MS01005"],"award-info":[{"award-number":["2024JQKY2","NJZY22215","2024MS01005"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we study three kinds of dentabilities and present their important applications in the geometric theory of Banach spaces. First, the relations between weak-denting points and extreme points are established. Moreover, we characterize strong convex spaces and weakly locally uniformly smooth spaces by using weakly locally uniform dentability. Finally, we provide some important applications of strong\u2217 dentability in Fr\u00e9chet-smooth Banach spaces while investigating the density of strong\u2217 points in dual Banach spaces.<\/jats:p>","DOI":"10.3390\/axioms14040306","type":"journal-article","created":{"date-parts":[[2025,4,16]],"date-time":"2025-04-16T11:02:57Z","timestamp":1744801377000},"page":"306","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Three Kinds of Denting Points and Their Further Applications in Banach Spaces"],"prefix":"10.3390","volume":"14","author":[{"given":"Xiaoxia","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematics and Computer Engineering, Ordos Institute of Technology, Ordos 017000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6756-2233","authenticated-orcid":false,"given":"Yunan","family":"Cui","sequence":"additional","affiliation":[{"name":"Faculty of Mathematic, Harbin Cambridge University, Harbin 150069, China"}]},{"given":"Yaoming","family":"Niu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Engineering, Ordos Institute of Technology, Ordos 017000, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,16]]},"reference":[{"key":"ref_1","unstructured":"Rieffel, M.A. (April, January 28). 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