. In this paper, in order to investigate a Gronwall inequality with state-dependence, another auxiliary map-type Gronwall inequality is discussed by modifying the technique of sequential monotonization on functions into the one on maps. Then we employ the state-dependent Gronwall inequality to give the estimate and boundedness of solutions for a functional differential equation with state-dependence. Finally, we exhibit a concrete example of bounded solutions as application.
{"title":"A map-type Gronwall inequality on functional differential equations with state-dependence","authors":"Jun Zhou","doi":"10.7153/jmi-2023-17-08","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-08","url":null,"abstract":". In this paper, in order to investigate a Gronwall inequality with state-dependence, another auxiliary map-type Gronwall inequality is discussed by modifying the technique of sequential monotonization on functions into the one on maps. Then we employ the state-dependent Gronwall inequality to give the estimate and boundedness of solutions for a functional differential equation with state-dependence. Finally, we exhibit a concrete example of bounded solutions as application.","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":"71166107","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}
Choonkill Park, A. Najati, M. B. Moghimi, B. Noori
. In this paper, we study the Ulam stability and hyperstability of two general functional equations in several variables in 2-Banach spaces. Multi-additive and multi-Jensen functions are particular cases of these functional equations. We also improve the main results of Theorem 3 and Theorem 4 of [Ciepli´nski, K. Ulam stability of functional equations in 2-Banach spaces via the fi xed point method. J. Fixed Point Theory Appl. 23 (2021
． 本文研究了2-Banach空间中两个多变量泛函方程的Ulam稳定性和超稳定性。多加性和多延森函数是这些函数方程的特殊情况。利用不动点法改进了2-Banach空间中泛函方程稳定性[Ciepli ' nski, K. Ulam]定理3和定理4的主要结果。[j] .不动点理论应用，23 (2021)
{"title":"Approximation of two general functional equations in 2-Banach spaces","authors":"Choonkill Park, A. Najati, M. B. Moghimi, B. Noori","doi":"10.7153/jmi-2023-17-11","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-11","url":null,"abstract":". In this paper, we study the Ulam stability and hyperstability of two general functional equations in several variables in 2-Banach spaces. Multi-additive and multi-Jensen functions are particular cases of these functional equations. We also improve the main results of Theorem 3 and Theorem 4 of [Ciepli´nski, K. Ulam stability of functional equations in 2-Banach spaces via the fi xed point method. J. Fixed Point Theory Appl. 23 (2021","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":"71166184","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, by proving some monotonicity theorems of certain combinations of the arc lemniscate sine function and elementary functions, we obtain two classes of exponential type inequalities for the arc lemniscate sine function. As applications, sharp bounds for the lemniscatic mean in terms of the arithmetic, harmonic and geometric means are given, which extend some previously known results.
{"title":"Sharp exponential type inequalities for the arc lemniscate sine function with applications","authors":"Jinl ng Niu, Miao-Kun Wang, Wei-Mao Qian, Yuming Chu, Hui-Zuo Xu","doi":"10.7153/jmi-2023-17-33","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-33","url":null,"abstract":". In this paper, by proving some monotonicity theorems of certain combinations of the arc lemniscate sine function and elementary functions, we obtain two classes of exponential type inequalities for the arc lemniscate sine function. As applications, sharp bounds for the lemniscatic mean in terms of the arithmetic, harmonic and geometric means are given, which extend some previously known results.","PeriodicalId":49165,"journal":{"name":"Journal of Mathematical Inequalities","volume":"228 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71166322","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 concept of the Davis-Wielandt Berezin number is introduced. Some upper and lower bounds for the Davis-Wielandt Berezin number are introduced. A connection between norm-parallelism to the identity operator and an equality condition for the Davis-Wielandt Berezin number are also discussed. Some bounds for the Davis-Wielandt Berezin number for n × n operator matrices are established.
{"title":"Norm-parallelism of Hilbert space operators and the Davis-Wielandt Berezin number","authors":"M. Alomari, M. Hajmohamadi, M. Bakherad","doi":"10.7153/jmi-2023-17-17","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-17","url":null,"abstract":". In this work, the concept of the Davis-Wielandt Berezin number is introduced. Some upper and lower bounds for the Davis-Wielandt Berezin number are introduced. A connection between norm-parallelism to the identity operator and an equality condition for the Davis-Wielandt Berezin number are also discussed. Some bounds for the Davis-Wielandt Berezin number for n × n operator matrices are established.","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":"71166421","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}
Yuming Chu, M. U. Awan, Sadia Talib, M. Noor, K. Noor
. We derive two new fractional quantum integral identities. Using these identities we obtain several new fractional quantum estimates of trapezoid like inequalities essentially using the class of preinvex functions.
{"title":"Fractional quantum analogues of trapezoid like inequalities","authors":"Yuming Chu, M. U. Awan, Sadia Talib, M. Noor, K. Noor","doi":"10.7153/jmi-2023-17-03","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-03","url":null,"abstract":". We derive two new fractional quantum integral identities. Using these identities we obtain several new fractional quantum estimates of trapezoid like inequalities essentially using the class of preinvex functions.","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":"71165542","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}
. Convex functions have a key role in mathematical inequalities. In this paper, we employ radical convexity as a tool that enables us to obtain much sharper bounds than usual bounds obtained by convexity. Applications of our approach will include real functions and matrices
{"title":"Improved matrix inequalities using radical convexity","authors":"M. Sababheh, S. Furuichi, H. Moradi","doi":"10.7153/jmi-2023-17-24","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-24","url":null,"abstract":". Convex functions have a key role in mathematical inequalities. In this paper, we employ radical convexity as a tool that enables us to obtain much sharper bounds than usual bounds obtained by convexity. Applications of our approach will include real functions and matrices","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":"71166134","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":"Another proof of Hrölder's inequality","authors":"Seo ho Jin, Kwang Seob Kim","doi":"10.7153/jmi-2023-17-13","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-13","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":"71166296","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 study the mapping properties of singular integral operators along surfaces of revo-lutions on product domains. For several classes of surfaces, we prove sharp L p bounds ( 1 < p < ) for these singular integral operators as well as their corresponding maximal operators. By using these L p bounds and an extrapolation argument we obtain the L p boundedness of these operators under optimal conditions on the singular kernels. Our results extend and improve several results previously obtained by many authors.
． 研究了乘积域上沿旋转曲面的奇异积分算子的映射性质。对于几类曲面，我们证明了这些奇异积分算子及其对应的极大算子的锐利的L p界(1 < p <)。在奇异核的最优条件下，利用这些算子的L - p界和一个外推论证，得到了这些算子的L - p有界性。我们的结果扩展和改进了许多作者以前得到的一些结果。
{"title":"On singular integrals and maximal operators along surfaces of revolution on product domains","authors":"AL Hussain, Qassem, L. Cheng","doi":"10.7153/jmi-2023-17-48","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-48","url":null,"abstract":". We study the mapping properties of singular integral operators along surfaces of revo-lutions on product domains. For several classes of surfaces, we prove sharp L p bounds ( 1 < p < ) for these singular integral operators as well as their corresponding maximal operators. By using these L p bounds and an extrapolation argument we obtain the L p boundedness of these operators under optimal conditions on the singular kernels. Our results extend and improve several results previously obtained by many authors.","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":"71166704","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":"Nonexistence and existence of positive ground state solutions for generalized quasilinear Schrödinger equations","authors":"Yunf ng Wei, Caish ng Chen, Hongw ng Yu, Rui Hu","doi":"10.7153/jmi-2023-17-52","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-52","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":"71166809","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":"On several inequalities related to convex functions","authors":"Nicuşor Minculete","doi":"10.7153/jmi-2023-17-70","DOIUrl":"https://doi.org/10.7153/jmi-2023-17-70","url":null,"abstract":"","PeriodicalId":49165,"journal":{"name":"Journal of Mathematical Inequalities","volume":"116 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":"135002955","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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