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Mathematical Inequalities & Applications最新文献

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Best constant of the critical Hardy-Leray inequality for curl-free fields in two dimensions 二维无旋度场临界Hardy-Leray不等式的最佳常数
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2021-01-01 DOI: 10.7153/MIA-2021-24-27
N. Hamamoto, F. Takahashi
{"title":"Best constant of the critical Hardy-Leray inequality for curl-free fields in two dimensions","authors":"N. Hamamoto, F. Takahashi","doi":"10.7153/MIA-2021-24-27","DOIUrl":"https://doi.org/10.7153/MIA-2021-24-27","url":null,"abstract":". In this note, we prove that the best-possible constant of the critical Hardy-Leray in- equality for curl-free fi elds is 1 / 4, just the same value as the one for all smooth fi elds. This fact contrasts sharply with the recent result on the subcritical Hardy-Leray inequality for curl-free fi elds by the authors [6], and shows the criticality of the inequality.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71204122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
The orthogonal projections and several inequalities 正交投影和几个不等式
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2021-01-01 DOI: 10.7153/MIA-2021-24-13
N. Minculete, M. Niezgoda
{"title":"The orthogonal projections and several inequalities","authors":"N. Minculete, M. Niezgoda","doi":"10.7153/MIA-2021-24-13","DOIUrl":"https://doi.org/10.7153/MIA-2021-24-13","url":null,"abstract":"In this article we study several inequalities related to the orthogonal projections and we established new results related to a pre-Hilbert space. Among these results we will mention the inequality of Ostrowski. We present an improvement of the inequality between the numerical radius of an operator and the norm of an operator and we also show other inequalities for a bounded linear operator. Finally, we show Grüss type inequalities on double ice-cream cones. Mathematics subject classification (2010): 46C05, 26D10, 26D15.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71204157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Remarks on the monotonicity and convexity of Jensen's function 简森函数的单调性和凸性
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2021-01-01 DOI: 10.7153/MIA-2021-24-37
Yang Huang, Yong ao Li, J. Pečarić
{"title":"Remarks on the monotonicity and convexity of Jensen's function","authors":"Yang Huang, Yong ao Li, J. Pečarić","doi":"10.7153/MIA-2021-24-37","DOIUrl":"https://doi.org/10.7153/MIA-2021-24-37","url":null,"abstract":". Let x 1 , x 2 ,... , x n be nonnegative real numbers. The Jensen function of { x i } i = 1 is de fi ned as J s ( x ) = ( ∑ in = 1 x is ) 1 / s , also known as the L p -norm. It is well-known that J s ( x ) is decreasing on s ∈ ( 0 , + ∞ ) . Moreover, Beckenbach [Amer. Math. Monthly, 53 (1946), 501– 505] proved further that J s ( x ) is a convex function on s ∈ ( 0 , + ∞ ) . The goal of this note is two-fold. We fi rst revisit the skillful treatment of the proof of Beckenbach, and then we simplify the proof slightly. Additionally, we give a new proof of the convexity of J s ( x ) by using the H¨older inequality, our proof is more succinct and short. On the other hand, we investigate a Jensen-type inequality that arised from Fourier analysis by Stein and Weiss. As a byproduct, the Hardy-Littlewood-P´oya inequality is also included. (2010):","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71204245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Necessary and sufficient conditions for a difference constituted by four derivatives of a function involving trigamma function to be completely monotonic 含三角函数的四阶导数构成的差是完全单调的充分必要条件
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2021-01-01 DOI: 10.7153/mia-2021-24-58
Feng Qi (祁锋)
{"title":"Necessary and sufficient conditions for a difference constituted by four derivatives of a function involving trigamma function to be completely monotonic","authors":"Feng Qi (祁锋)","doi":"10.7153/mia-2021-24-58","DOIUrl":"https://doi.org/10.7153/mia-2021-24-58","url":null,"abstract":"In the paper, by virtue of convolution theorem for the Laplace transforms, Bernstein’s theorem for completely monotonic functions, and other techniques, the author finds necessary and sufficient conditions for a difference constituted by four derivatives of a function involving trigamma function to be completely monotonic. Mathematics subject classification (2020): Primary 33B15; Secondary 26A48, 26A51, 26D07, 44A10.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71204473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Weighted norm inequalities for the generalized multilinear Stieltjes transformation 广义多线性Stieltjes变换的加权范数不等式
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2021-01-01 DOI: 10.7153/mia-2021-24-53
Víctor García García, P. O. Salvador
{"title":"Weighted norm inequalities for the generalized multilinear Stieltjes transformation","authors":"Víctor García García, P. O. Salvador","doi":"10.7153/mia-2021-24-53","DOIUrl":"https://doi.org/10.7153/mia-2021-24-53","url":null,"abstract":". We characterize some weighted strong and weak-type inequalities for the generalized Stieltjes and Calder´on multilinear operators. As applications, we characterize a weighted multilinear Hilbert’s inequality and a weighted Hilbert’s multiple series theorem.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71204680","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On L_p intersection mean ellipsoids and affine isoperimetric inequalities L_p交平均椭球与仿射等周不等式
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2021-01-01 DOI: 10.7153/mia-2021-24-75
X. Cai, Fangwei Chen
{"title":"On L_p intersection mean ellipsoids and affine isoperimetric inequalities","authors":"X. Cai, Fangwei Chen","doi":"10.7153/mia-2021-24-75","DOIUrl":"https://doi.org/10.7153/mia-2021-24-75","url":null,"abstract":"","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71204785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The upper boundary for the ratio between n-variable operator power means 上界为n变量算子幂均值之比
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2021-01-01 DOI: 10.7153/mia-2021-24-52
Y. Seo
{"title":"The upper boundary for the ratio between n-variable operator power means","authors":"Y. Seo","doi":"10.7153/mia-2021-24-52","DOIUrl":"https://doi.org/10.7153/mia-2021-24-52","url":null,"abstract":"","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71204852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On a Mercer like inequality involving generalized Csiszár f-divergences 关于广义Csiszár f散度的类美塞不等式
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2021-01-01 DOI: 10.7153/MIA-2021-24-08
M. Niezgoda
{"title":"On a Mercer like inequality involving generalized Csiszár f-divergences","authors":"M. Niezgoda","doi":"10.7153/MIA-2021-24-08","DOIUrl":"https://doi.org/10.7153/MIA-2021-24-08","url":null,"abstract":". In this note, an upper bound for values of a convex function f is shown for some speci fi c arguments of the function. Thus a Mercer like inequality involving generalized Csisz´ar f -divergences is obtained. Special cases of the result are studied. Mathematics","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71203727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On constants in coconvex approximation of periodic functions 周期函数共凸逼近中的常数
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2021-01-01 DOI: 10.7153/MIA-2021-24-14
G. Dzyubenko
{"title":"On constants in coconvex approximation of periodic functions","authors":"G. Dzyubenko","doi":"10.7153/MIA-2021-24-14","DOIUrl":"https://doi.org/10.7153/MIA-2021-24-14","url":null,"abstract":". Let 2 π -periodic function f ∈ C change its convexity fi nitely even many times, in the period. We are interested in estimating the degree of approximation of f by trigonometric polynomials which are coconvex with it, namely, polynomials that change their convexity exactly at the points where f does. We list established Jackson-type estimates of such approximation where the constants involved depend on the location of the points of change of convexity and show that this dependence is essential by constructing a counterexample.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"97 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71204173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Inequalities for quermassintegrals of (new) p-parallel bodies (新)p-平行体的质量积分不等式
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2021-01-01 DOI: 10.7153/mia-2021-24-78
Yingying Lou, Zhenb ng Zeng
{"title":"Inequalities for quermassintegrals of (new) p-parallel bodies","authors":"Yingying Lou, Zhenb ng Zeng","doi":"10.7153/mia-2021-24-78","DOIUrl":"https://doi.org/10.7153/mia-2021-24-78","url":null,"abstract":"","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71204431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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