R. Tinaztepe, G. Tinaztepe, Zeynep Eken, Sevda Sezer, S. Kemali, Ilknur Yesilce Isik, S. S. Evcan
{"title":"The sharper version for generalized power mean inequalities with negative exponent","authors":"R. Tinaztepe, G. Tinaztepe, Zeynep Eken, Sevda Sezer, S. Kemali, Ilknur Yesilce Isik, S. S. Evcan","doi":"10.7153/jmi-2023-17-07","DOIUrl":null,"url":null,"abstract":". In this study, the generalized power mean inequalities with a negative parameter are re fi ned using an optimality theorem on the generator function. The optimality theorem requires the study of different cases for the exponents and yields a re fi nement of the inequality in a neighbourhood of the vectors for which the equality occurs. Then, these local inequalities are generalized to all positive vectors by an appropriate selection of parameters. Also, some of the results are exempli fi ed by numerical calculations.","PeriodicalId":49165,"journal":{"name":"Journal of Mathematical Inequalities","volume":"1 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Inequalities","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7153/jmi-2023-17-07","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
. In this study, the generalized power mean inequalities with a negative parameter are re fi ned using an optimality theorem on the generator function. The optimality theorem requires the study of different cases for the exponents and yields a re fi nement of the inequality in a neighbourhood of the vectors for which the equality occurs. Then, these local inequalities are generalized to all positive vectors by an appropriate selection of parameters. Also, some of the results are exempli fi ed by numerical calculations.
期刊介绍:
The ''Journal of Mathematical Inequalities'' (''JMI'') presents carefully selected original research articles from all areas of pure and applied mathematics, provided they are concerned with mathematical inequalities and their numerous applications. ''JMI'' will also periodically publish invited survey articles and short notes with interesting results treating the theory of inequalities, as well as relevant book reviews. Only articles written in the English language and in a lucid, expository style will be considered for publication. ''JMI'' primary audience are pure mathematicians, applied mathemathicians and numerical analysts.
''JMI'' is published quarterly; in March, June, September, and December.