{"title":"集值余弦族的交换性","authors":"A. Smajdor, W. Smajdor","doi":"10.2478/s11533-014-0433-y","DOIUrl":null,"url":null,"abstract":"Let K be a closed convex cone with nonempty interior in a real Banach space and let cc(K) denote the family of all nonempty convex compact subsets of K. If {Ft: t ≥ 0} is a regular cosine family of continuous additive set-valued functions Ft: K → cc(K) such that x ∈ Ft(x) for t ≥ 0 and x ∈ K, then $F_t \\circ F_s (x) = F_s \\circ F_t (x)fors,t \\geqslant 0andx \\in K$.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"33 1","pages":"1871-1881"},"PeriodicalIF":0.0000,"publicationDate":"2014-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Commutativity of set-valued cosine families\",\"authors\":\"A. Smajdor, W. Smajdor\",\"doi\":\"10.2478/s11533-014-0433-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let K be a closed convex cone with nonempty interior in a real Banach space and let cc(K) denote the family of all nonempty convex compact subsets of K. If {Ft: t ≥ 0} is a regular cosine family of continuous additive set-valued functions Ft: K → cc(K) such that x ∈ Ft(x) for t ≥ 0 and x ∈ K, then $F_t \\\\circ F_s (x) = F_s \\\\circ F_t (x)fors,t \\\\geqslant 0andx \\\\in K$.\",\"PeriodicalId\":50988,\"journal\":{\"name\":\"Central European Journal of Mathematics\",\"volume\":\"33 1\",\"pages\":\"1871-1881\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-07-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Central European Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2478/s11533-014-0433-y\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Central European Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/s11533-014-0433-y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Let K be a closed convex cone with nonempty interior in a real Banach space and let cc(K) denote the family of all nonempty convex compact subsets of K. If {Ft: t ≥ 0} is a regular cosine family of continuous additive set-valued functions Ft: K → cc(K) such that x ∈ Ft(x) for t ≥ 0 and x ∈ K, then $F_t \circ F_s (x) = F_s \circ F_t (x)fors,t \geqslant 0andx \in K$.