{"title":"Two lower bounds for the smallest singular value of matrices","authors":"Wushu ng Liu, Xing ai Hu, Ya qun Wang, Yuan Yi","doi":"10.7153/jmi-2023-17-56","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-56","url":null,"abstract":"","PeriodicalId":49165,"journal":{"name":"Journal of Mathematical Inequalities","volume":"17 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":"136373743","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}
R. Tinaztepe, G. Tinaztepe, Zeynep Eken, Sevda Sezer, S. Kemali, Ilknur Yesilce Isik, S. S. Evcan
. 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.
{"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":"https://doi.org/10.7153/jmi-2023-17-07","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":2.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71165699","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 prove that some Hiroshima’s type inequalities for positive semidefinite block matrices are equivalent. These interesting results are due to Hiroshima [Phys. Rev. Lett. 91 , (2003), 057902], Lin and Wolkowicz [Linear Multilinear Algebra 60 , 11–12 (2012), 1365–1368], Turkmen, Paksoy and Zhang [Linear Algebra Appl. 437 , 6 (2012), 1305–1316], Zhang and Xu [J. Math. Inequal. 14 , 4 (2020), 1383–1388], respectively.
{"title":"Equivalence on Hiroshima's type inequalities for positive semidefinite block matrices","authors":"Yun Zhang, Ha bo Zhang, Shuo Shi","doi":"10.7153/jmi-2023-17-23","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-23","url":null,"abstract":". In this paper, we prove that some Hiroshima’s type inequalities for positive semidefinite block matrices are equivalent. These interesting results are due to Hiroshima [Phys. Rev. Lett. 91 , (2003), 057902], Lin and Wolkowicz [Linear Multilinear Algebra 60 , 11–12 (2012), 1365–1368], Turkmen, Paksoy and Zhang [Linear Algebra Appl. 437 , 6 (2012), 1305–1316], Zhang and Xu [J. Math. Inequal. 14 , 4 (2020), 1383–1388], respectively.","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":"71166076","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}
. The present paper deals with “the perturbation of Legendre eigenvalue problem” with limit-circle type non-oscillation endpoints. The dissipative operators in limit-circle case are studied. Lower bounds on the real parts of all eigenvalues and the upper bounds on the imaginary parts of the non-real eigenvalues for this eigenvalue problem associated to a special separated boundary condition (see the below in ( ?? )) are obtained through a new method, partly inspired by the estimates obtained in Sun and Qi (Proc. Roy. Soc. Edinburgh A, 150:2607-2619, 2020).
{"title":"The bounds of eigenvalue for complex singular boundary value problems","authors":"Fu Sun, Xiao ue Han","doi":"10.7153/jmi-2023-17-09","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-09","url":null,"abstract":". The present paper deals with “the perturbation of Legendre eigenvalue problem” with limit-circle type non-oscillation endpoints. The dissipative operators in limit-circle case are studied. Lower bounds on the real parts of all eigenvalues and the upper bounds on the imaginary parts of the non-real eigenvalues for this eigenvalue problem associated to a special separated boundary condition (see the below in ( ?? )) are obtained through a new method, partly inspired by the estimates obtained in Sun and Qi (Proc. Roy. Soc. Edinburgh A, 150:2607-2619, 2020).","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":"71166120","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}
. This paper studies the stochastic evolution equations with fi nite delay. By means of the compact semigroup theory and Schauder fi xed point theorem, the existence of square-mean S -asymptotically periodic mild solutions is obtained under certain growth conditions. In addition, using the contraction mapping principle and Gronwall integral inequality, the uniqueness and global asymptotic stability of the square-mean S -asymptotically periodic mild solutions are discussed. Finally, an example is given to illustrate our abstract results.
{"title":"Existence and asymptotic behavior of square-mean S-asymptotically periodic solutions for stochastic evolution equation involving delay","authors":"Qiang Li, Xuan Wu","doi":"10.7153/jmi-2023-17-26","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-26","url":null,"abstract":". This paper studies the stochastic evolution equations with fi nite delay. By means of the compact semigroup theory and Schauder fi xed point theorem, the existence of square-mean S -asymptotically periodic mild solutions is obtained under certain growth conditions. In addition, using the contraction mapping principle and Gronwall integral inequality, the uniqueness and global asymptotic stability of the square-mean S -asymptotically periodic mild solutions are discussed. Finally, an example is given to illustrate our abstract results.","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":"71166155","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}
. By making use of the basic properties of Laplace-Stieltjes transform, we establish some inequalities concerning the abscissa of convergence, the abscissa of absolute convergence and the abscissa of uniform convergence of Laplace-Stieltjes transform (cid:2) ∞ 0 e st d α ( t ) . Moreover, we point out that our formulas for the three abscissas of convergence are consistent with the previous results given by Yu [26] for Laplace-Stieltjes transform under some conditions.
． 利用Laplace-Stieltjes变换的基本性质，建立了Laplace-Stieltjes变换(cid:2)∞0 est d α (t)的收敛横坐标、绝对收敛横坐标和一致收敛横坐标的不等式。此外，我们还指出，在某些条件下，我们的三个坐标的收敛性公式与Yu[26]给出的拉普拉斯-斯蒂尔杰斯变换的结果是一致的。
{"title":"Some inequalities on the convergent abscissas of Laplace-Stieltjes transforms","authors":"H. Xu, Z. Xuan","doi":"10.7153/jmi-2023-17-12","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-12","url":null,"abstract":". By making use of the basic properties of Laplace-Stieltjes transform, we establish some inequalities concerning the abscissa of convergence, the abscissa of absolute convergence and the abscissa of uniform convergence of Laplace-Stieltjes transform (cid:2) ∞ 0 e st d α ( t ) . Moreover, we point out that our formulas for the three abscissas of convergence are consistent with the previous results given by Yu [26] for Laplace-Stieltjes transform under some conditions.","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":"71166228","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 work, the complete moment convergence for weighted sums of negatively associated random variables is discussed without assumptions of identical distribution. Under the moment condition E | X | / ( log ( 1 + | X | )) / − 1 < for the case 0 < < with 1 < (cid:2) 2, the complete moment convergence theorem for weighted sums of negatively associated setup is presented. The main results obtained in this article extend and improve the corresponding ones of Chen and Sung (Stat. Probabil. Lett., 92: 45–52 (2014)), Sung (Stat. Pap., 52: 447–454 (2011)).
． 本文讨论了负相关随机变量加权和的完全矩收敛性，不考虑相同分布的假设。在矩条件E | X |/ (log (1 + | X |))/−1 <对于0 <<且1 <(cid:2) 2的情况下，给出了负相关设置加权和的完全矩收敛定理。本文得到的主要结果是对Chen和Sung (Stat. probil)的相应结果的推广和改进。列托人。[j] .科学通报，2014(2):45-52。农业学报，52:447-454(2011))。
{"title":"On complete moment convergence for weighted sums under negatively associated setup","authors":"Haiwu Huang, Yanc un Yi, Xiong ao Wu","doi":"10.7153/jmi-2023-17-39","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-39","url":null,"abstract":". In this work, the complete moment convergence for weighted sums of negatively associated random variables is discussed without assumptions of identical distribution. Under the moment condition E | X | / ( log ( 1 + | X | )) / − 1 < for the case 0 < < with 1 < (cid:2) 2, the complete moment convergence theorem for weighted sums of negatively associated setup is presented. The main results obtained in this article extend and improve the corresponding ones of Chen and Sung (Stat. Probabil. Lett., 92: 45–52 (2014)), Sung (Stat. Pap., 52: 447–454 (2011)).","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":"71166434","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 obtain some improvements and generalizations of Young’s inequalities as the following:
． 本文对杨氏不等式作了一些改进和推广:
{"title":"Some new improvements of Young's inequalities","authors":"Changsen Yang, Zhenq an Wang","doi":"10.7153/jmi-2023-17-15","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-15","url":null,"abstract":". In this paper, we obtain some improvements and generalizations of Young’s inequalities as the following:","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":"71166473","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}
M. Vivas-Cortez, A. Kashuri, Muhammad Raees, M. Anwar
{"title":"New quantum integral inequalities via m-convex functions over finite interval","authors":"M. Vivas-Cortez, A. Kashuri, Muhammad Raees, M. Anwar","doi":"10.7153/jmi-2023-17-45","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-45","url":null,"abstract":"","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":"71166629","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":"Complete convergence and complete moment convergence for weighted sums of m-extended negatively dependent random variables","authors":"Xiang Huang, Yongf ng Wu","doi":"10.7153/jmi-2023-17-46","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-46","url":null,"abstract":"","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":"71166641","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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