{"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}
{"title":"Weighted Hellinger distance and in-betweenness property","authors":"T. Dinh, C. Lê, B. K. Vo, T. Vuong","doi":"10.7153/MIA-2021-24-11","DOIUrl":"https://doi.org/10.7153/MIA-2021-24-11","url":null,"abstract":"In this paper we introduce the weighted Hellinger distance for matrices which is an interpolating between the Euclidean distance and the Hellinger distance. We show the equivalence of the weighted Hellinger distance and the Alpha Procrustes distance. As a consequence, we prove that the matrix power mean μp(t,A,B) = (tAp +(1−t)Bp)1/p satisfies in-betweenness property in the weighted Hellinger and Alpha Procrustes distances. Mathematics subject classification (2010): 47A63, 47A56.","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":"71203514","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}
{"title":"Composition operators and closures of a class of Möbius invariant function spaces in the Bloch space","authors":"L. X. Zhang","doi":"10.7153/MIA-2021-24-04","DOIUrl":"https://doi.org/10.7153/MIA-2021-24-04","url":null,"abstract":". Closures of a class of M¨obius invariant function spaces in the Bloch space are investi- gated in this paper. Moreover, the boundedness and compactness of composition operators from the Bloch space to closures of such M¨obius invariant space in the Bloch space are characterized. Mathematics subject classi fi cation (2010): 30H30, 30H99, 47B33.","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":"71203670","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}
{"title":"Bounds for indices of coincidence and entropies","authors":"A. Acu, Gülen Başcanbaz-Tunca, I. Raşa","doi":"10.7153/MIA-2021-24-22","DOIUrl":"https://doi.org/10.7153/MIA-2021-24-22","url":null,"abstract":". In this paper we consider a parameterized family of discrete probability distributions and investigate the R´enyi,Tsallis, and Shannon entropies associated with them. Lower and upper bounds for these entropies are obtained, improving some results from the literature. The proofs are based on several methods from classical analysis, theory of dual cones, and the stochastic majorization theory. The R´enyi and Tsallis entropies are naturally expressed in terms of the index of coincidence. Consequently we study in detail the index of coincidence associated to the corresponding discrete probability distributions. The obtained results lead immediately to properties of the entropies.","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":"71204077","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}
{"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}
{"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}
{"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}
{"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}
{"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}
{"title":"Some Hardy-type inequalities in Banach function spaces","authors":"Sorina Barza, L. Nikolova, L. Persson, M. Yimer","doi":"10.7153/mia-2021-24-70","DOIUrl":"https://doi.org/10.7153/mia-2021-24-70","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":"71204704","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}