. In the article, we present the best possible parameters α
． 在本文中，我们给出了最佳可能参数α
{"title":"Sharp inequalities for the Toader mean of order -1 in terms of other bivariate means","authors":"Wei-Mao Qian, Hong-Hu Chu, Miao-Kun Wang, Yuming Chu","doi":"10.7153/jmi-2022-16-10","DOIUrl":"https://doi.org/10.7153/jmi-2022-16-10","url":null,"abstract":". In the article, we present the best possible parameters α","PeriodicalId":49165,"journal":{"name":"Journal of Mathematical Inequalities","volume":"37 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71164104","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":"A fractional magnetic Hardy-Sobolev inequality with two variables","authors":"Min Liu, De an Chen, Zhe yu Guo","doi":"10.7153/jmi-2022-16-14","DOIUrl":"https://doi.org/10.7153/jmi-2022-16-14","url":null,"abstract":"","PeriodicalId":49165,"journal":{"name":"Journal of Mathematical Inequalities","volume":"1 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71164322","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}
. A new generalization of Whittaker function M λ , µ ( z ) is introduced and studied by means of the extended multi-index confluent hypergeometric function of the first kind Φ ( γ i ) , p ( α i , β i ) introduced in [1]. The related Euler–type integral representation and the Laplace–Mellin and Hankel integral transforms are also presented. Functional two–sided bounding inequality is established for the multi-index Mittag-Leffler function, and in continuation functional lower bound is derived for the associated ML-extended Whittaker function.
． 利用[1]中引入的第一类扩展多指数合流超几何函数Φ (γ i)， p (α i， β i)，给出了Whittaker函数M λ，µ(z)的一个新的推广。给出了相关的欧拉型积分表示和Laplace-Mellin和Hankel积分变换。建立了多指标Mittag-Leffler函数的泛函双面边界不等式，并推导了相应的ml扩展Whittaker函数的泛函下界。
{"title":"On multi-index Whittaker function, related integrals and inequalities","authors":"Musharraf Ali, J. Paneva-Konovska, T. Pogány","doi":"10.7153/jmi-2022-16-37","DOIUrl":"https://doi.org/10.7153/jmi-2022-16-37","url":null,"abstract":". A new generalization of Whittaker function M λ , µ ( z ) is introduced and studied by means of the extended multi-index confluent hypergeometric function of the first kind Φ ( γ i ) , p ( α i , β i ) introduced in [1]. The related Euler–type integral representation and the Laplace–Mellin and Hankel integral transforms are also presented. Functional two–sided bounding inequality is established for the multi-index Mittag-Leffler function, and in continuation functional lower bound is derived for the associated ML-extended Whittaker function.","PeriodicalId":49165,"journal":{"name":"Journal of Mathematical Inequalities","volume":"1 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71164515","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":"Deviation estimations for Lotka-Nagaev estimator of a branching process with immigration","authors":"Deqi ng Yuan, Zhenl ng Gao","doi":"10.7153/jmi-2022-16-43","DOIUrl":"https://doi.org/10.7153/jmi-2022-16-43","url":null,"abstract":"","PeriodicalId":49165,"journal":{"name":"Journal of Mathematical Inequalities","volume":"1 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71164636","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}
Let A(a,b) , G(a,b) , L (a,b) and TQ(a,b) be the arithmetic, geometric, logarithmic and Toader-Qi means of a,b > 0 with a = b , respectively. Let Iv (x) be the modified Bessel functions of the first kind of order v . We prove the double inequality √ sinh t t Uq (t) < I0 (t) < √ sinh t t Up (t) holds for t > 0 , or equivalently, √ L (a,b)Uq (a,b) < TQ(a,b) < √ L (a,b)Up (a,b), holds for a,b > 0 with a = b , if and only if p 11/15 and 0 < q 2/π , where Up (t) = pcosh t−4 ( p− 2 3 )
设A(A,b)、G(A,b)、L (A,b)和TQ(A,b)分别为A,b和b的算术均值、几何均值、对数均值和Toader-Qi均值。设Iv (x)是第一类v阶的修正贝塞尔函数。我们证明了二重不等式√sinh t t Uq (t) < I0 (t) <√sinh t t Up (t)对t >成立，或者等价地，√L (a,b)Uq (a,b) < TQ(a,b) <√L (a,b)Up (a,b)，当且仅当p 11/15和0 < q 2/π，其中Up (t) = pcosh t−4 (p−2 3)，当a = b时，对a,b >成立。
{"title":"On new sharp bounds for the Toader-Qi mean involved in the modified Bessel functions of the first kind","authors":"Cen Li, Zhi-Ming Liu, Shenzhou Zheng","doi":"10.7153/jmi-2022-16-44","DOIUrl":"https://doi.org/10.7153/jmi-2022-16-44","url":null,"abstract":"Let A(a,b) , G(a,b) , L (a,b) and TQ(a,b) be the arithmetic, geometric, logarithmic and Toader-Qi means of a,b > 0 with a = b , respectively. Let Iv (x) be the modified Bessel functions of the first kind of order v . We prove the double inequality √ sinh t t Uq (t) < I0 (t) < √ sinh t t Up (t) holds for t > 0 , or equivalently, √ L (a,b)Uq (a,b) < TQ(a,b) < √ L (a,b)Up (a,b), holds for a,b > 0 with a = b , if and only if p 11/15 and 0 < q 2/π , where Up (t) = pcosh t−4 ( p− 2 3 )","PeriodicalId":49165,"journal":{"name":"Journal of Mathematical Inequalities","volume":"1 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71164688","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 paper is concerned with H ( Z ) -eigenvalues of the solution of the Lyapunov ten- sor equation. According to the Lyapunov algebraic theorem on tensors, bounds for H ( Z ) eigenvalues of the solution are given fi rstly, then based on the relationship between the Lya- punov tensor equation and the continuous-time linear uncertain system, conditional inequalities for the asymptotic stability of the system are shown by H ( Z ) -eigenvalues of the solution of the Lyapunov tensor equation.
{"title":"Eigenvalues of the solution of the Lyapunov tensor equation","authors":"L. Liang","doi":"10.7153/jmi-2022-16-46","DOIUrl":"https://doi.org/10.7153/jmi-2022-16-46","url":null,"abstract":". The paper is concerned with H ( Z ) -eigenvalues of the solution of the Lyapunov ten- sor equation. According to the Lyapunov algebraic theorem on tensors, bounds for H ( Z ) eigenvalues of the solution are given fi rstly, then based on the relationship between the Lya- punov tensor equation and the continuous-time linear uncertain system, conditional inequalities for the asymptotic stability of the system are shown by H ( Z ) -eigenvalues of the solution of the Lyapunov tensor equation.","PeriodicalId":49165,"journal":{"name":"Journal of Mathematical Inequalities","volume":"1 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71164711","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":"Threshold dynamics behaviors of a stochastic SIRS epidemic model with a parameter functional value","authors":"Jian uo Sun, Miaom ao Gao","doi":"10.7153/jmi-2022-16-52","DOIUrl":"https://doi.org/10.7153/jmi-2022-16-52","url":null,"abstract":"","PeriodicalId":49165,"journal":{"name":"Journal of Mathematical Inequalities","volume":"1 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71165080","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}
. Let ϕ be an analytic self-map of the open unit disk D and let ψ be an analytic function on D . The weighted composition operator C ψ , ϕ is the operator on the Hardy space H 2 given by C ψ , ϕ f = ψ f ◦ ϕ . Under some conditions on ϕ 1 and ϕ 2 , we try to fi nd a subset of the numerical range of C ψ 1 , ϕ 1 + C ψ 2 , ϕ 2 and determine when zero lies in the interior of the numerical range of C ψ 1 , ϕ 1 + C ψ 2 , ϕ 2 .
{"title":"Numerical ranges of sum of two weighted composition operators on the Hardy space H^2","authors":"M. H. Shaabani, Narjes Vafaei","doi":"10.7153/jmi-2022-16-92","DOIUrl":"https://doi.org/10.7153/jmi-2022-16-92","url":null,"abstract":". Let ϕ be an analytic self-map of the open unit disk D and let ψ be an analytic function on D . The weighted composition operator C ψ , ϕ is the operator on the Hardy space H 2 given by C ψ , ϕ f = ψ f ◦ ϕ . Under some conditions on ϕ 1 and ϕ 2 , we try to fi nd a subset of the numerical range of C ψ 1 , ϕ 1 + C ψ 2 , ϕ 2 and determine when zero lies in the interior of the numerical range of C ψ 1 , ϕ 1 + C ψ 2 , ϕ 2 .","PeriodicalId":49165,"journal":{"name":"Journal of Mathematical Inequalities","volume":"1 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71165785","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":"The nonexistence of extremals for the Hardy-Trudinger-Moser inequality in the hyperbolic space","authors":"Qian in Luo","doi":"10.7153/jmi-2022-16-08","DOIUrl":"https://doi.org/10.7153/jmi-2022-16-08","url":null,"abstract":"","PeriodicalId":49165,"journal":{"name":"Journal of Mathematical Inequalities","volume":"1 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71164027","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}
Hüseyin Aktuğlu, Halil Gezer, Erdem Baytunç, M. S. Atamert
. In this paper, we introduce a family of blending type Bernstein operators L α , s n ( f ; x ) which depends on two parameters, α and s . We prove a Korovkin type approximation theorem and obtain the rate of convergence of these operators. We also prove that these operators has monotonicity and convexity preserving properties for each α and s . So far, Lotosky matrices that generates blending type Bernstein operators were ignored. In this paper, we also introduce Lototsky matrices that generates these new family of blending type Bernstein operators.
。本文引入了一类混合型Bernstein算子L α， s n (f;X)，它取决于两个参数，α和s。我们证明了一个Korovkin型近似定理，并得到了这些算子的收敛速率。我们还证明了这些算子对每个α和s都具有单调性和凸性。到目前为止，忽略了生成混合型Bernstein算子的Lotosky矩阵。在本文中，我们还引入了生成这些新的混合型Bernstein算子族的Lototsky矩阵。
{"title":"Approximation properties of generalized blending type Lototsky-Bernstein operators","authors":"Hüseyin Aktuğlu, Halil Gezer, Erdem Baytunç, M. S. Atamert","doi":"10.7153/jmi-2022-16-50","DOIUrl":"https://doi.org/10.7153/jmi-2022-16-50","url":null,"abstract":". In this paper, we introduce a family of blending type Bernstein operators L α , s n ( f ; x ) which depends on two parameters, α and s . We prove a Korovkin type approximation theorem and obtain the rate of convergence of these operators. We also prove that these operators has monotonicity and convexity preserving properties for each α and s . So far, Lotosky matrices that generates blending type Bernstein operators were ignored. In this paper, we also introduce Lototsky matrices that generates these new family of blending type Bernstein operators.","PeriodicalId":49165,"journal":{"name":"Journal of Mathematical Inequalities","volume":"1 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71164995","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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