{"title":"集值映射的上、下方向导数集和微分","authors":"Nihal Ege, A. Huseyin, N. Huseyin","doi":"10.35634/vm220304","DOIUrl":null,"url":null,"abstract":"In this paper directional derivative sets and differentials of a given set valued map are studied. Different type relations between directional derivative sets and differentials of a set valued map are specified. It is established that every compact subset of lower derivative set can be used for lower approximation of given set valued map. Upper and lower contingent cones of some plane sets are calculated and compared.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Upper and lower directional derivative sets and differentials of the set valued maps\",\"authors\":\"Nihal Ege, A. Huseyin, N. Huseyin\",\"doi\":\"10.35634/vm220304\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper directional derivative sets and differentials of a given set valued map are studied. Different type relations between directional derivative sets and differentials of a set valued map are specified. It is established that every compact subset of lower derivative set can be used for lower approximation of given set valued map. Upper and lower contingent cones of some plane sets are calculated and compared.\",\"PeriodicalId\":43239,\"journal\":{\"name\":\"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2022-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.35634/vm220304\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.35634/vm220304","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Upper and lower directional derivative sets and differentials of the set valued maps
In this paper directional derivative sets and differentials of a given set valued map are studied. Different type relations between directional derivative sets and differentials of a set valued map are specified. It is established that every compact subset of lower derivative set can be used for lower approximation of given set valued map. Upper and lower contingent cones of some plane sets are calculated and compared.
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