. In this paper we present estimation formulas for the expectations of power means of large data and associate them with means of probability distribution and means of random sample. The proposed method follows from the asymptotic expansion of power means which is applicable for suf fi ciently large data and it is especially useful when value of such expectation is hard to obtain. We will show the accuracy of these approximations for random samples which have uniform and normal distribution and analyse their behaviour for large sample volume.
{"title":"Expectations of large data means","authors":"Tomislav Buric, N. Elezovic, Lenka Mihoković","doi":"10.7153/jmi-2023-17-27","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-27","url":null,"abstract":". In this paper we present estimation formulas for the expectations of power means of large data and associate them with means of probability distribution and means of random sample. The proposed method follows from the asymptotic expansion of power means which is applicable for suf fi ciently large data and it is especially useful when value of such expectation is hard to obtain. We will show the accuracy of these approximations for random samples which have uniform and normal distribution and analyse their behaviour for large sample volume.","PeriodicalId":49165,"journal":{"name":"Journal of Mathematical Inequalities","volume":"1 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71166198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Further refinements of the Tan-Xie inequality for sector matrices and its applications","authors":"Yong ui Ren","doi":"10.7153/jmi-2023-17-78","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-78","url":null,"abstract":"","PeriodicalId":49165,"journal":{"name":"Journal of Mathematical Inequalities","volume":"80 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135002611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Numerical radius of products of special matrices","authors":"Mohammad Alakhrass","doi":"10.7153/jmi-2023-17-64","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-64","url":null,"abstract":"","PeriodicalId":49165,"journal":{"name":"Journal of Mathematical Inequalities","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135002635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study some properties such as the monotonicity, logarithmically complete monotonicity, logarithmic convexity, and geometric convexity, of the combinations of gamma function and power function. The results we obtain generalize some related known results for parameters with specific values.
{"title":"Monotonicity, convexity, and inequalities for functions involving gamma function","authors":"Pei ei Du, Gendi Wang","doi":"10.7153/jmi-2023-17-67","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-67","url":null,"abstract":"In this paper, we study some properties such as the monotonicity, logarithmically complete monotonicity, logarithmic convexity, and geometric convexity, of the combinations of gamma function and power function. The results we obtain generalize some related known results for parameters with specific values.","PeriodicalId":49165,"journal":{"name":"Journal of Mathematical Inequalities","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136372941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Further properties of 2-inner product spaces","authors":"Abbas Alipour, Mohammad Hadi Akhbari","doi":"10.7153/jmi-2023-17-75","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-75","url":null,"abstract":"","PeriodicalId":49165,"journal":{"name":"Journal of Mathematical Inequalities","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136372978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Sharp bound of m-linear n-dimensional p-adic Hausdorff operators on p-adic Morrey spaces","authors":"Xi an Zhang, Qian un He, Xi ng Li","doi":"10.7153/jmi-2023-17-79","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-79","url":null,"abstract":"","PeriodicalId":49165,"journal":{"name":"Journal of Mathematical Inequalities","volume":"148 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136373189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tao Zhang, Alatancang Chen, Bo-Yan Xi, Huan-Nan Shi
{"title":"The relationship between r-convexity and Schur-convexity and its application","authors":"Tao Zhang, Alatancang Chen, Bo-Yan Xi, Huan-Nan Shi","doi":"10.7153/jmi-2023-17-74","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-74","url":null,"abstract":"","PeriodicalId":49165,"journal":{"name":"Journal of Mathematical Inequalities","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136373195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We assume that the forecast error follows a probability distribution which is symmetric and monotonically non-increasing on non-negative real numbers, and if there is a mismatch between observed and predicted value, then we suffer a loss. Under the assumptions, we solve a minimization problem with an asymmetric loss function. In addition, we give an inequality for the variance of the loss.
{"title":"Inequality for the variance of an asymmetric loss","authors":"Naoya Yamaguchi, Yuka Yamaguchi, Maiya Hori","doi":"10.7153/jmi-2023-17-58","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-58","url":null,"abstract":"We assume that the forecast error follows a probability distribution which is symmetric and monotonically non-increasing on non-negative real numbers, and if there is a mismatch between observed and predicted value, then we suffer a loss. Under the assumptions, we solve a minimization problem with an asymmetric loss function. In addition, we give an inequality for the variance of the loss.","PeriodicalId":49165,"journal":{"name":"Journal of Mathematical Inequalities","volume":"165 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136373500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. In this paper, we de fi ne the commutators of fractional integral operators and Calder´on-Zygmund singular integral operators on differential forms, and give the suf fi cient and necessary conditions for these commutators to be bounded on weighted Lebesgue spaces. As an application, the Caccioppoli-type inequalities with Orlicz norm for commutators of Calder´on-Zygmund singular integral operators on differential forms are obtained.
{"title":"Inequalities for commutators of fractional integrals and singular integrals on differential forms","authors":"Jinl ng Niu, Guan an Shi, S. Ding, Yuming Xing","doi":"10.7153/jmi-2023-17-28","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-28","url":null,"abstract":". In this paper, we de fi ne the commutators of fractional integral operators and Calder´on-Zygmund singular integral operators on differential forms, and give the suf fi cient and necessary conditions for these commutators to be bounded on weighted Lebesgue spaces. As an application, the Caccioppoli-type inequalities with Orlicz norm for commutators of Calder´on-Zygmund singular integral operators on differential forms are obtained.","PeriodicalId":49165,"journal":{"name":"Journal of Mathematical Inequalities","volume":"1 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71166207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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