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We show that the dual cones, related to the metric projection and generalized metric projection, lose many important properties in transitioning from Hilbert spaces to Banach spaces. We also propose and analyze the notions of faces and visions in Banach spaces and relate them to metric projection and generalized projection. We provide many illustrative examples to give insight into the given results<\/jats:p>","DOI":"10.1007\/s11590-024-02126-9","type":"journal-article","created":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T04:01:30Z","timestamp":1718078490000},"page":"389-412","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Dual and generalized dual cones in Banach spaces"],"prefix":"10.1007","volume":"19","author":[{"given":"Akhtar A.","family":"Khan","sequence":"first","affiliation":[]},{"given":"Dezhou","family":"Kong","sequence":"additional","affiliation":[]},{"given":"Jinlu","family":"Li","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,6,11]]},"reference":[{"key":"2126_CR1","unstructured":"Alber, Y.I.: Generalized projection operators in Banach spaces: properties and applications. In: Functional-Differential Equations, Funct. 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