{"title":"改进了度量空间中距离的不等式","authors":"S. Dragomir","doi":"10.31926/but.mif.2022.2.64.2.5","DOIUrl":null,"url":null,"abstract":"In this note we prove among others that\n∑1≤i<j≤npipjdS(xi,xj)≤ {2s−1 infx∈X [ Σ k=1n pk (1 − pk) ds (xk, x)], s ≥ 1; infx∈X [ Σ k=1n pk (1 − pk) ds (xk, x)] , 0 < s < 1, where (X, d) is a metric space, xi ∈ X, pi ≥ 0, i ∈ {1, ..., n} with Σ i=1n pi = 1 and s > 0. This generalizes and improves some early upper bounds for the sum Σ1≤i<j≤n pipjd (xi, xj) .","PeriodicalId":53266,"journal":{"name":"Bulletin of the Transilvania University of Brasov Series V Economic Sciences","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Refined inequalities for the distance in metric spaces\",\"authors\":\"S. Dragomir\",\"doi\":\"10.31926/but.mif.2022.2.64.2.5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this note we prove among others that\\n∑1≤i<j≤npipjdS(xi,xj)≤ {2s−1 infx∈X [ Σ k=1n pk (1 − pk) ds (xk, x)], s ≥ 1; infx∈X [ Σ k=1n pk (1 − pk) ds (xk, x)] , 0 < s < 1, where (X, d) is a metric space, xi ∈ X, pi ≥ 0, i ∈ {1, ..., n} with Σ i=1n pi = 1 and s > 0. This generalizes and improves some early upper bounds for the sum Σ1≤i<j≤n pipjd (xi, xj) .\",\"PeriodicalId\":53266,\"journal\":{\"name\":\"Bulletin of the Transilvania University of Brasov Series V Economic Sciences\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-12-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the Transilvania University of Brasov Series V Economic Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.31926/but.mif.2022.2.64.2.5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Transilvania University of Brasov Series V Economic Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31926/but.mif.2022.2.64.2.5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}