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Mathematical Inequalities & Applications最新文献

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Exact lower and upper bounds on the incomplete gamma function 不完全gamma函数的精确下界和上界
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2020-05-13 DOI: 10.7153/mia-2020-23-95
I. Pinelis
{"title":"Exact lower and upper bounds on the incomplete gamma function","authors":"I. Pinelis","doi":"10.7153/mia-2020-23-95","DOIUrl":"https://doi.org/10.7153/mia-2020-23-95","url":null,"abstract":"Lower and upper bounds $B_a(x)$ on the incomplete gamma function $Gamma(a,x)$ are given for all real $a$ and all real $x>0$. These bounds $B_a(x)$ are exact in the sense that $B_a(x)underset{xdownarrow0}simGamma(a,x)$ and $B_a(x)underset{xtoinfty}simGamma(a,x)$. Moreover, the relative errors of these bounds are rather small for other values of $x$, away from $0$ and $infty$.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43172538","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: 18
Direct and inverse approximation theorems of functions in the Musielak-Orlicz type spaces Musielak-Orlicz型空间中函数的正逼近和逆逼近定理
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2020-04-21 DOI: 10.7153/mia-2021-24-23
F. Abdullayev, S. Chaichenko, A. Shidlich
{"title":"Direct and inverse approximation theorems of functions in the Musielak-Orlicz type spaces","authors":"F. Abdullayev, S. Chaichenko, A. Shidlich","doi":"10.7153/mia-2021-24-23","DOIUrl":"https://doi.org/10.7153/mia-2021-24-23","url":null,"abstract":"In Musilak-Orlicz type spaces ${mathcal S}_{bf M}$, direct and inverse approximation theorems are obtained in terms of the best approximations of functions and generalized moduli of smoothness. The question of the exact constants in Jackson-type inequalities is studied.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41519131","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: 8
Joint numerical radius of spherical Aluthge transforms of tuples of Hilbert space operators Hilbert空间算子元组的球面Aluthge变换的联合数值半径
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2020-04-06 DOI: 10.7153/MIA-2021-24-28
Kais Feki, Takeaki Yamazaki
{"title":"Joint numerical radius of spherical Aluthge transforms of tuples of Hilbert space operators","authors":"Kais Feki, Takeaki Yamazaki","doi":"10.7153/MIA-2021-24-28","DOIUrl":"https://doi.org/10.7153/MIA-2021-24-28","url":null,"abstract":"Let $mathbf{T}=(T_1,ldots,T_d)$ be a $d$-tuple of operators on a complex Hilbert space $mathcal{H}$. The spherical Aluthge transform of $mathbf{T}$ is the $d$-tuple given by $widehat{mathbf{T}}:=(sqrt{P}V_1sqrt{P},ldots,sqrt{P}V_dsqrt{P})$ where $P:=sqrt{T_1^*T_1+ldots+T_d^*T_d}$ and $(V_1,ldots,V_d)$ is a joint partial isometry such that $T_k=V_k P$ for all $1 le k le d$. In this paper, we prove several inequalities involving the joint numerical radius and the joint operator norm of $widehat{mathbf{T}}$. Moreover, a characterization of the joint spectral radius of an operator tuple $mathbf{T}$ via $n$-th iterated of spherical Aluthge transform is established.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42096114","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: 11
Further subadditive matrix inequalities 进一步的次加性矩阵不等式
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2020-04-01 DOI: 10.7153/mia-2020-23-86
I. Gumus, H. Moradi, M. Sababheh
{"title":"Further subadditive matrix inequalities","authors":"I. Gumus, H. Moradi, M. Sababheh","doi":"10.7153/mia-2020-23-86","DOIUrl":"https://doi.org/10.7153/mia-2020-23-86","url":null,"abstract":"Matrix inequalities that extend certain scalar ones have been in the center of numerous researchers' attention. In this article, we explore the celebrated subadditive inequality for matrices via concave functions and present a reversed version of this result. Our approach will be tackling concave functions properties and some delicate manipulations of matrices and inner product properties. Once this has been done, concavity approach is implemented to show many sub and super additive inequalities for the determinant. This approach is a new direction in this type of inequalities. In the end, many determinant inequalities are presented for accretive-dissipative matrices.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46032544","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
Monotonicity of weighted averages of convex functions 凸函数加权平均的单调性
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2020-04-01 DOI: 10.7153/MIA-2020-23-33
G. Jameson
{"title":"Monotonicity of weighted averages of convex functions","authors":"G. Jameson","doi":"10.7153/MIA-2020-23-33","DOIUrl":"https://doi.org/10.7153/MIA-2020-23-33","url":null,"abstract":"We consider weighted averages of the form Bn(W, f ) = ∑r=0 wn,r f (r/n) , where W is a summability matrix and f is convex. Conditions are given for Bn(W, f ) to increase or decrease with n . It decreases whenever W is a Hausdorff mean. The sequence of Bernstein polynomials for a convex function is a special case. Mathematics subject classification (2010): 26D15, 40G05, 41A10.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"1 1","pages":"425-432"},"PeriodicalIF":1.0,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43395064","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: 3
Interactions between Hlawka Type-1 and Type-2 quantities Hlawka 1型和2型量之间的相互作用
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2020-03-13 DOI: 10.7153/mia-2021-24-63
Xin Luo
{"title":"Interactions between Hlawka Type-1 and Type-2 quantities","authors":"Xin Luo","doi":"10.7153/mia-2021-24-63","DOIUrl":"https://doi.org/10.7153/mia-2021-24-63","url":null,"abstract":"The classical Hlawka inequality possesses deep connections with zonotopes and zonoids in convex geometry, and has been related to Minkowski space. We introduce Hlawka Type-1 and Type-2 quantities, and establish a Hlawka-type relation between them, which connects a vast number of strikingly different variants of the Hlawka inequalities, such as Serre’s reverse Hlawka inequality in the future cone of the Minkowski space, the Hlawka inequality for subadditive function on abelian group by Ressel, and the integral analogs by Takahasi et al. Besides, we announce several en-hanced results, such as the Hlawka inequality for the power of measure function. Particularly, we give a complete study of the Hlawka inequality for quadratic form which relates to a work of Serre.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44480240","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 regarding partial trace and partial determinant 关于部分迹和部分行列式的不等式
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2020-01-08 DOI: 10.7153/mia-2020-23-39
Yongtao Li, Lihua Feng, Zheng Huang, Weijun Liu
{"title":"Inequalities regarding partial trace and partial determinant","authors":"Yongtao Li, Lihua Feng, Zheng Huang, Weijun Liu","doi":"10.7153/mia-2020-23-39","DOIUrl":"https://doi.org/10.7153/mia-2020-23-39","url":null,"abstract":"In this paper, we first present simple proofs of Choi's results [4], then we give a short alternative proof for Fiedler and Markham's inequality [6]. We also obtain additional matrix inequalities related to partial determinants.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43354270","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: 8
Inequalities for angles between subspaces with applications to Cauchy-Schwarz inequality in inner product spaces 子空间间角的不等式及其内积空间中Cauchy-Schwarz不等式的应用
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2020-01-01 DOI: 10.7153/mia-2020-23-40
Z. Otachel
{"title":"Inequalities for angles between subspaces with applications to Cauchy-Schwarz inequality in inner product spaces","authors":"Z. Otachel","doi":"10.7153/mia-2020-23-40","DOIUrl":"https://doi.org/10.7153/mia-2020-23-40","url":null,"abstract":"We show several inequalities for angles between vectors and subspaces in inner product spaces, where concave functions are involved. In specific situations, some of them can be interpreted as triangle inequalities for natural metrics on complex projective spaces. In a consequence, we obtain a few operator generalizations of the famous Cauchy-Schwarz inequality, where powers grater than two occur. Mathematics subject classification (2010): 46C05, 15A455.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"1 1","pages":"487-495"},"PeriodicalIF":1.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71202194","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
Equivalent statements of a more accurate extended Mulholland's inequality with a best possible constant factor 一个具有最佳可能常数因子的更精确的扩展穆赫兰不等式的等价表述
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2020-01-01 DOI: 10.7153/mia-2020-23-18
Bicheng Yang, Me fa Huang, Y. Zhong
{"title":"Equivalent statements of a more accurate extended Mulholland's inequality with a best possible constant factor","authors":"Bicheng Yang, Me fa Huang, Y. Zhong","doi":"10.7153/mia-2020-23-18","DOIUrl":"https://doi.org/10.7153/mia-2020-23-18","url":null,"abstract":"By the use of the weight functions, the idea of introduced parameters and HermiteHadamard’s inequality, a more accurate extended Mulholland’s inequality and its equivalent form are given. A few equivalent statements of the best possible constant factor related to some parameters, some particular cases and the operator expressions are considered. Mathematics subject classification (2010): 26D15.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"1 1","pages":"231-244"},"PeriodicalIF":1.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71202226","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 estimates of multilinear fractional integral operators for radial functions 径向函数的多线性分数阶积分算子的加权估计
IF 1 4区 数学
Mathematical Inequalities & Applications Pub Date : 2020-01-01 DOI: 10.7153/mia-2020-23-19
Y. Komori‐Furuya, Enji Sato
{"title":"Weighted estimates of multilinear fractional integral operators for radial functions","authors":"Y. Komori‐Furuya, Enji Sato","doi":"10.7153/mia-2020-23-19","DOIUrl":"https://doi.org/10.7153/mia-2020-23-19","url":null,"abstract":"Moen (2009) proved weighted estimates for multilinear fractional integral operators. We consider weighted estimates of these operators for radial functions and power weights and obtain a better result. Our result is a multilinear variant of the one by De Napoli, Drelichman and Durán (2011). As applications, we get improvements of the bilinear Caffarelli-Kohn-Nirenberg’s inequality. Mathematics subject classification (2010): 42B20.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"1 1","pages":"245-256"},"PeriodicalIF":1.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71202374","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
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