Viacheslav Kalashnikov, A. Talman, N. Kalashnykova, L. Alanís-López
{"title":"对跖型定理的扩展","authors":"Viacheslav Kalashnikov, A. Talman, N. Kalashnykova, L. Alanís-López","doi":"10.1109/UMSO.2018.8637224","DOIUrl":null,"url":null,"abstract":"The paper develops the extensions of both the antipodal (Borsuk–Ulam) theorem and Browder theorem to the cases embracing star-shaped domains of the studied mappings and a multi-valued nature of the latter.To be more specific, by making use of the triangulation procedure, we spread out the antipodal and fixed-point theorems to the case of not necessarily convex (star-shaped) domains. In addition, similar extensions are obtained for multi-valued mappings defined over star-shaped sets. Moreover, a directt algorithm shaping the required connected path of the zero points of the mapping has been designed, and its convergence demonstrated.","PeriodicalId":433225,"journal":{"name":"2018 International Conference on Unconventional Modelling, Simulation and Optimization - Soft Computing and Meta Heuristics - UMSO","volume":"33 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Extensions of Antipodal-Type Theorems\",\"authors\":\"Viacheslav Kalashnikov, A. Talman, N. Kalashnykova, L. Alanís-López\",\"doi\":\"10.1109/UMSO.2018.8637224\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The paper develops the extensions of both the antipodal (Borsuk–Ulam) theorem and Browder theorem to the cases embracing star-shaped domains of the studied mappings and a multi-valued nature of the latter.To be more specific, by making use of the triangulation procedure, we spread out the antipodal and fixed-point theorems to the case of not necessarily convex (star-shaped) domains. In addition, similar extensions are obtained for multi-valued mappings defined over star-shaped sets. Moreover, a directt algorithm shaping the required connected path of the zero points of the mapping has been designed, and its convergence demonstrated.\",\"PeriodicalId\":433225,\"journal\":{\"name\":\"2018 International Conference on Unconventional Modelling, Simulation and Optimization - Soft Computing and Meta Heuristics - UMSO\",\"volume\":\"33 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2018 International Conference on Unconventional Modelling, Simulation and Optimization - Soft Computing and Meta Heuristics - UMSO\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/UMSO.2018.8637224\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2018 International Conference on Unconventional Modelling, Simulation and Optimization - Soft Computing and Meta Heuristics - UMSO","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/UMSO.2018.8637224","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The paper develops the extensions of both the antipodal (Borsuk–Ulam) theorem and Browder theorem to the cases embracing star-shaped domains of the studied mappings and a multi-valued nature of the latter.To be more specific, by making use of the triangulation procedure, we spread out the antipodal and fixed-point theorems to the case of not necessarily convex (star-shaped) domains. In addition, similar extensions are obtained for multi-valued mappings defined over star-shaped sets. Moreover, a directt algorithm shaping the required connected path of the zero points of the mapping has been designed, and its convergence demonstrated.
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