T. Sow, M. Ndiaye, M. Sene, N. Djitté
{"title":"Banach空间中非线性单调映射的零点计算","authors":"T. Sow, M. Ndiaye, M. Sene, N. Djitté","doi":"10.16929/SBS/2018.100-03-02","DOIUrl":null,"url":null,"abstract":"Let E be a uniformly convex real Banach space with uniformly Gâteaux differentiable norm and E∗ its dual space and let A : E → E∗ be a bounded and uniformly monotone mapping such that A−1(0) 6= ∅. In this paper, we introduce an new explicit iterative algorithm that converges strongly to the unique zeros of A . The results proved here are applied to the convex optimization problem. keywords. Uniformly monotone Mapping; zeros of mappings; Iterative algorithms . AMS 2010 Mathematics Subject Classification. 47H04; 47H06; 47H15; 47H17; 47J25 Cite the paper as : Sow T.M, Ndiaye M., Sene M. and Djitte, N. (2018). Computation of zeros of nonlinear monotone mappings in certain Banach spaces. In A Collection of Papers in Mathematics and Related Sciences, a festschrift in honour of the late Galaye Dia (Editors : Seydi H., Lo G.S. and Diakhaby A.). Spas Editions, Euclid Series Book, pp. 257 –273. Doi : 10.16929/sbs/2018.100-03-02 c ©Spas Editions, Saint-Louis Calgary 2018 H. Seydi et al. (Eds.) A Collection of Papers in Mathematics and Related Sciences, a festschrift in honour of the late Galaye Dia. Doi : 10.16929/sbs/2018.100","PeriodicalId":321019,"journal":{"name":"A Collection of Papers in Mathematics and Related Sciences, a festschrift in honour of the late Galaye Dia","volume":"11 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Computation of zeros of nonlinear monotone mappings in certain Banach spaces\",\"authors\":\"T. Sow, M. Ndiaye, M. Sene, N. Djitté\",\"doi\":\"10.16929/SBS/2018.100-03-02\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let E be a uniformly convex real Banach space with uniformly Gâteaux differentiable norm and E∗ its dual space and let A : E → E∗ be a bounded and uniformly monotone mapping such that A−1(0) 6= ∅. In this paper, we introduce an new explicit iterative algorithm that converges strongly to the unique zeros of A . The results proved here are applied to the convex optimization problem. keywords. Uniformly monotone Mapping; zeros of mappings; Iterative algorithms . AMS 2010 Mathematics Subject Classification. 47H04; 47H06; 47H15; 47H17; 47J25 Cite the paper as : Sow T.M, Ndiaye M., Sene M. and Djitte, N. (2018). Computation of zeros of nonlinear monotone mappings in certain Banach spaces. In A Collection of Papers in Mathematics and Related Sciences, a festschrift in honour of the late Galaye Dia (Editors : Seydi H., Lo G.S. and Diakhaby A.). Spas Editions, Euclid Series Book, pp. 257 –273. Doi : 10.16929/sbs/2018.100-03-02 c ©Spas Editions, Saint-Louis Calgary 2018 H. Seydi et al. (Eds.) A Collection of Papers in Mathematics and Related Sciences, a festschrift in honour of the late Galaye Dia. Doi : 10.16929/sbs/2018.100\",\"PeriodicalId\":321019,\"journal\":{\"name\":\"A Collection of Papers in Mathematics and Related Sciences, a festschrift in honour of the late Galaye Dia\",\"volume\":\"11 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-12-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"A Collection of Papers in Mathematics and Related Sciences, a festschrift in honour of the late Galaye Dia\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.16929/SBS/2018.100-03-02\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"A Collection of Papers in Mathematics and Related Sciences, a festschrift in honour of the late Galaye Dia","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.16929/SBS/2018.100-03-02","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Computation of zeros of nonlinear monotone mappings in certain Banach spaces
Let E be a uniformly convex real Banach space with uniformly Gâteaux differentiable norm and E∗ its dual space and let A : E → E∗ be a bounded and uniformly monotone mapping such that A−1(0) 6= ∅. In this paper, we introduce an new explicit iterative algorithm that converges strongly to the unique zeros of A . The results proved here are applied to the convex optimization problem. keywords. Uniformly monotone Mapping; zeros of mappings; Iterative algorithms . AMS 2010 Mathematics Subject Classification. 47H04; 47H06; 47H15; 47H17; 47J25 Cite the paper as : Sow T.M, Ndiaye M., Sene M. and Djitte, N. (2018). Computation of zeros of nonlinear monotone mappings in certain Banach spaces. In A Collection of Papers in Mathematics and Related Sciences, a festschrift in honour of the late Galaye Dia (Editors : Seydi H., Lo G.S. and Diakhaby A.). Spas Editions, Euclid Series Book, pp. 257 –273. Doi : 10.16929/sbs/2018.100-03-02 c ©Spas Editions, Saint-Louis Calgary 2018 H. Seydi et al. (Eds.) A Collection of Papers in Mathematics and Related Sciences, a festschrift in honour of the late Galaye Dia. Doi : 10.16929/sbs/2018.100
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