{"title":"JENSEN不等式的推广与精化","authors":"F. Rubab, Hira Nabi, Asif R. Khan","doi":"10.54379/jma-2021-5-1","DOIUrl":null,"url":null,"abstract":"We give generalizations and refinements of Jensen and Jensen− Mercer inequalities by using weights which satisfy the conditions of Jensen and Jensen− Steffensen inequalities. We also give some refinements for discrete and integral version of generalized Jensen−Mercer inequality and shown to be an improvement of the upper bound for the Jensen’s difference given in [32]. Applications of our work include new bounds for some important inequalities used in information theory, and generalizing the relations among means.","PeriodicalId":45467,"journal":{"name":"Journal of Mathematical Analysis","volume":"1 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2021-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"GENERALIZATION AND REFINEMENTS OF JENSEN INEQUALITY\",\"authors\":\"F. Rubab, Hira Nabi, Asif R. Khan\",\"doi\":\"10.54379/jma-2021-5-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We give generalizations and refinements of Jensen and Jensen− Mercer inequalities by using weights which satisfy the conditions of Jensen and Jensen− Steffensen inequalities. We also give some refinements for discrete and integral version of generalized Jensen−Mercer inequality and shown to be an improvement of the upper bound for the Jensen’s difference given in [32]. Applications of our work include new bounds for some important inequalities used in information theory, and generalizing the relations among means.\",\"PeriodicalId\":45467,\"journal\":{\"name\":\"Journal of Mathematical Analysis\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2021-10-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.54379/jma-2021-5-1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.54379/jma-2021-5-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
GENERALIZATION AND REFINEMENTS OF JENSEN INEQUALITY
We give generalizations and refinements of Jensen and Jensen− Mercer inequalities by using weights which satisfy the conditions of Jensen and Jensen− Steffensen inequalities. We also give some refinements for discrete and integral version of generalized Jensen−Mercer inequality and shown to be an improvement of the upper bound for the Jensen’s difference given in [32]. Applications of our work include new bounds for some important inequalities used in information theory, and generalizing the relations among means.
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