ABSTRACT In this paper, we provide Dirichlet series with periodic coefficients that have Riemann’s functional equation and real zeros of Dirichlet L-functions. The details are as follows. Let L ( s, χ ) be the Dirichlet L -function and G ( χ ) be the Gauss sum associated with a primitive Dirichlet character χ (mod q ). We define f(s,χ):=qsL(s,χ)+i−κ(χ)G(χ)L(s,χ¯) , where χ¯ is the complex conjugate of χ and κ ( χ ) := (1 – χ (−1))/2. Then, we prove that f ( s , χ ) satisfies Riemann’s functional equation in Hamburger’s theorem if χ is even. In addition, we show that f ( σ , χ ) ≠ 0 for all σ ≥ 1. Moreover, we prove that f ( σ , χ ) ≠ 0 for all 1/2 ≤ σ < 1 if and only if L ( σ , χ ) ≠ 0 for all 1/2 ≤ σ < 1. When χ is real, all zeros of f ( s , χ ) with ℜ(s)>0 are on the line σ = 1/2 if and only if the generalized Riemann hypothesis for L ( s , χ ) is true. However, f ( s , χ ) has infinitely many zeros off the critical line σ = 1/2 if χ is non-real.
本文给出了具有Riemann泛函方程和Dirichlet l -函数实零的周期系数Dirichlet级数。具体情况如下。设L (s， χ)为狄利克雷L函数，G (χ)为与原始狄利克雷字符χ (mod q)相关的高斯和。我们定义f (s， χ):= q s L (s， χ) + i−κ (χ) G (χ) L (s， χ¯)，其中χ¯是χ和κ (χ):= (1 - χ(−1))/2的复共轭。然后，我们证明了f (s， χ)在χ为偶数时满足汉堡包定理中的Riemann泛函方程。此外，我们证明了对于所有σ≥1,f (σ， χ)≠0。进一步证明了对于所有1/2≤σ <, f (σ， χ)≠0;1当且仅当L (σ， χ)≠0，对于所有1/2≤σ <1. 当χ为实数时，f (s， χ)与f (s) >均为零;当且仅当L (s， χ)的广义黎曼假设成立时，0在σ = 1/2线上。然而，如果χ是非实数，f (s， χ)在临界线σ = 1/2外有无穷多个零。
{"title":"Dirichlet Series with Periodic Coefficients, Riemann’s Functional Equation, and Real Zeros of Dirichlet <i>L</i>-Functions","authors":"Takashi Nakamura","doi":"10.1515/ms-2023-0084","DOIUrl":"https://doi.org/10.1515/ms-2023-0084","url":null,"abstract":"ABSTRACT In this paper, we provide Dirichlet series with periodic coefficients that have Riemann’s functional equation and real zeros of Dirichlet L-functions. The details are as follows. Let L ( s, χ ) be the Dirichlet L -function and G ( χ ) be the Gauss sum associated with a primitive Dirichlet character χ (mod q ). We define <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <m:mrow> <m:mi>f</m:mi> <m:mo stretchy=\"false\">(</m:mo> <m:mi>s</m:mi> <m:mo>,</m:mo> <m:mi>χ</m:mi> <m:mo stretchy=\"false\">)</m:mo> <m:mo>:</m:mo> <m:mo>=</m:mo> <m:msup> <m:mi>q</m:mi> <m:mi>s</m:mi> </m:msup> <m:mi>L</m:mi> <m:mo stretchy=\"false\">(</m:mo> <m:mi>s</m:mi> <m:mo>,</m:mo> <m:mi>χ</m:mi> <m:mo stretchy=\"false\">)</m:mo> <m:mo>+</m:mo> <m:msup> <m:mrow> <m:mtext> </m:mtext> <m:mtext>i</m:mtext> </m:mrow> <m:mrow> <m:mo>−</m:mo> <m:mi>κ</m:mi> <m:mo stretchy=\"false\">(</m:mo> <m:mi>χ</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:msup> <m:mi>G</m:mi> <m:mo stretchy=\"false\">(</m:mo> <m:mi>χ</m:mi> <m:mo stretchy=\"false\">)</m:mo> <m:mi>L</m:mi> <m:mo stretchy=\"false\">(</m:mo> <m:mi>s</m:mi> <m:mo>,</m:mo> <m:mover accent=\"true\"> <m:mi>χ</m:mi> <m:mo>¯</m:mo> </m:mover> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:math> , where <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <m:mover accent=\"true\"> <m:mi>χ</m:mi> <m:mo>¯</m:mo> </m:mover> </m:math> is the complex conjugate of χ and κ ( χ ) := (1 – χ (−1))/2. Then, we prove that f ( s , χ ) satisfies Riemann’s functional equation in Hamburger’s theorem if χ is even. In addition, we show that f ( σ , χ ) ≠ 0 for all σ ≥ 1. Moreover, we prove that f ( σ , χ ) ≠ 0 for all 1/2 ≤ σ < 1 if and only if L ( σ , χ ) ≠ 0 for all 1/2 ≤ σ < 1. When χ is real, all zeros of f ( s , χ ) with <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <m:mrow> <m:mi>ℜ</m:mi> <m:mo stretchy=\"false\">(</m:mo> <m:mi>s</m:mi> <m:mo stretchy=\"false\">)</m:mo> <m:mo>></m:mo> <m:mn>0</m:mn> </m:mrow> </m:math> are on the line σ = 1/2 if and only if the generalized Riemann hypothesis for L ( s , χ ) is true. However, f ( s , χ ) has infinitely many zeros off the critical line σ = 1/2 if χ is non-real.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135607032","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}
ABSTRACT In this work, a two-parameter continuous distribution, namely the Lehmann type II Teissier distribution is introduced. Some important properties including the Rényi entropy, Bonferroni curves, Lorenz curves and the exact information matrix of the proposed model are derived. Seven different techniques are being used for the estimation of parameters and a simulation is carried out to observe the maximum likelihood estimates. Interval estimates of the parameters are obtained using exact information matrix and bootstrapping techniques. Finally, to show the practical significance, three datasets related to COVID-19 and rainfall are modeled using the proposed model.
{"title":"The Lehmann Type II Teissier Distribution","authors":"V. Kumaran, Vishwa Prakash Jha","doi":"10.1515/ms-2023-0094","DOIUrl":"https://doi.org/10.1515/ms-2023-0094","url":null,"abstract":"ABSTRACT In this work, a two-parameter continuous distribution, namely the Lehmann type II Teissier distribution is introduced. Some important properties including the Rényi entropy, Bonferroni curves, Lorenz curves and the exact information matrix of the proposed model are derived. Seven different techniques are being used for the estimation of parameters and a simulation is carried out to observe the maximum likelihood estimates. Interval estimates of the parameters are obtained using exact information matrix and bootstrapping techniques. Finally, to show the practical significance, three datasets related to COVID-19 and rainfall are modeled using the proposed model.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135606299","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":"Remembering Professor Štefan Znám, 9.2.1936–17.7.1993","authors":"Peter Horák","doi":"10.1515/ms-2023-0080","DOIUrl":"https://doi.org/10.1515/ms-2023-0080","url":null,"abstract":"","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135606433","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}
ABSTRACT In this paper, we exhibit a rational parametric solution for the Diophantine equations of diagonal quartic varieties. Our approach is based on utilizing the Calabi-Yau varieties including elliptic curves and diagonal quartic surfaces.
{"title":"On the Rational Parametric Solution of Diagonal Quartic Varieties","authors":"Hassan Shabani-Solt, Amir Sarlak","doi":"10.1515/ms-2023-0085","DOIUrl":"https://doi.org/10.1515/ms-2023-0085","url":null,"abstract":"ABSTRACT In this paper, we exhibit a rational parametric solution for the Diophantine equations of diagonal quartic varieties. Our approach is based on utilizing the Calabi-Yau varieties including elliptic curves and diagonal quartic surfaces.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"98 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135606544","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}
ABSTRACT This paper is concerned with the oscillation criteria of odd-order non-linear differential equations with mixed non-linear neutral terms. We provide new oscillation criteria that improve, expand, and simplify existing ones. Moreover, some examples are provided to demonstrate the theoretical findings.
{"title":"Study of Oscillation Criteria of Odd-Order Differential Equations with Mixed Neutral Terms","authors":"Said R. Grace, Syed Abbas, Shekhar Singh Negi","doi":"10.1515/ms-2023-0091","DOIUrl":"https://doi.org/10.1515/ms-2023-0091","url":null,"abstract":"ABSTRACT This paper is concerned with the oscillation criteria of odd-order non-linear differential equations with mixed non-linear neutral terms. We provide new oscillation criteria that improve, expand, and simplify existing ones. Moreover, some examples are provided to demonstrate the theoretical findings.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"130 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135606545","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}
ABSTRACT Analytic expressions for the single and joint life annuities based on the Makeham–Beard mortality law have been derived recently in the literature, which depend on special mathematical functions such as hypergeometric functions. We verify that the arguments of the hypergeometric functions in the analytic expressions for the single and joint life annuities may assume values very close to unity (boundary of the convergence radius), and so numerical problems may arise when using them in practice. We provide, therefore, alternative analytic expressions for the single and joint life annuities where the arguments of the hypergeometric functions in the new analytic expressions do not assume values close to one.
{"title":"On Numerical Problems in Computing Life Annuities Based on the Makeham–Beard Law","authors":"Fredy Castellares, Artur J. Lemonte","doi":"10.1515/ms-2023-0096","DOIUrl":"https://doi.org/10.1515/ms-2023-0096","url":null,"abstract":"ABSTRACT Analytic expressions for the single and joint life annuities based on the Makeham–Beard mortality law have been derived recently in the literature, which depend on special mathematical functions such as hypergeometric functions. We verify that the arguments of the hypergeometric functions in the analytic expressions for the single and joint life annuities may assume values very close to unity (boundary of the convergence radius), and so numerical problems may arise when using them in practice. We provide, therefore, alternative analytic expressions for the single and joint life annuities where the arguments of the hypergeometric functions in the new analytic expressions do not assume values close to one.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135607036","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}
ABSTRACT We investigate the non-univalent function’s properties reminiscent of the theory of univalent starlike functions. Let the analytic function ψ(z)=∑i=1∞Aizi , A 1 ≠ 0 be univalent in the unitdisk. Non-univalent functions may be found in the class ℱ(ψ) of analytic functions f of the form f(z)=z+∑k=2∞akzk satisfying ( zf ′ ( z )/ f ( z ) – 1) ≺ ψ ( z ). Such functions, like the Ma and Minda classes k=2 of starlike functions, also have nice geometric properties. For these functions, growth and distortion theorems have been established. Further, we obtain bounds for some sharp coefficient functionals and establish the Bohr and Rogosinki phenomenon for the class ℱ(ψ) . Non-analytic functions that share properties of analytic functions are known as poly-analytic functions. Moreover, we compute Bohr and Rogosinski’s radius for poly-analytic functions with analytic counterparts in the class ℱ(ψ) or classes of Ma-Minda starlike and convex functions.
摘要研究了非一价函数的性质，使人联想到一价星形函数理论。设解析函数ψ (z) =∑i = 1∞A i z i, A 1≠0在单位圆盘上是一元的。在形式为f (z) = z +∑k = 2∞a k z k的解析函数f的类中，可以找到非一元函数满足(zf ' (z)/ f (z) - 1) ψ (z)。这样的函数，像星形函数的Ma和Minda类k=2，也有很好的几何性质。对于这些函数，建立了增长定理和畸变定理。进一步，我们得到了某些尖锐系数泛函的界，并建立了类的Bohr和Rogosinki现象。具有解析函数特性的非解析函数称为多解析函数。此外，我们还计算了具有解析对应物的多解析函数的玻尔半径和罗戈辛斯基半径，这些解析对应物在λ (ψ)类或马明达星形函数和凸函数类中。
{"title":"Theory of Certain Non-Univalent Analytic Functions","authors":"Kamaljeet Gangania","doi":"10.1515/ms-2023-0086","DOIUrl":"https://doi.org/10.1515/ms-2023-0086","url":null,"abstract":"ABSTRACT We investigate the non-univalent function’s properties reminiscent of the theory of univalent starlike functions. Let the analytic function <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <m:mrow> <m:mi>ψ</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mi>z</m:mi> <m:mo>)</m:mo> </m:mrow> <m:mo>=</m:mo> <m:mstyle displaystyle=\"true\"> <m:munderover> <m:mo>∑</m:mo> <m:mrow> <m:mi>i</m:mi> <m:mo>=</m:mo> <m:mn>1</m:mn> </m:mrow> <m:mi>∞</m:mi> </m:munderover> <m:mrow> <m:msub> <m:mi>A</m:mi> <m:mi>i</m:mi> </m:msub> <m:msup> <m:mi>z</m:mi> <m:mi>i</m:mi> </m:msup> </m:mrow> </m:mstyle> </m:mrow> </m:math> , A 1 ≠ 0 be univalent in the unitdisk. Non-univalent functions may be found in the class <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <m:mrow> <m:mi>ℱ</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mi>ψ</m:mi> <m:mo>)</m:mo> </m:mrow> </m:mrow> </m:math> of analytic functions f of the form <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <m:mrow> <m:mi>f</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mi>z</m:mi> <m:mo>)</m:mo> </m:mrow> <m:mo>=</m:mo> <m:mi>z</m:mi> <m:mo>+</m:mo> <m:mstyle displaystyle=\"true\"> <m:munderover> <m:mo>∑</m:mo> <m:mrow> <m:mi>k</m:mi> <m:mo>=</m:mo> <m:mn>2</m:mn> </m:mrow> <m:mi>∞</m:mi> </m:munderover> <m:mrow> <m:msub> <m:mi>a</m:mi> <m:mi>k</m:mi> </m:msub> <m:msup> <m:mi>z</m:mi> <m:mi>k</m:mi> </m:msup> </m:mrow> </m:mstyle> </m:mrow> </m:math> satisfying ( zf ′ ( z )/ f ( z ) – 1) ≺ ψ ( z ). Such functions, like the Ma and Minda classes k=2 of starlike functions, also have nice geometric properties. For these functions, growth and distortion theorems have been established. Further, we obtain bounds for some sharp coefficient functionals and establish the Bohr and Rogosinki phenomenon for the class <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <m:mrow> <m:mi>ℱ</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mi>ψ</m:mi> <m:mo>)</m:mo> </m:mrow> </m:mrow> </m:math> . Non-analytic functions that share properties of analytic functions are known as poly-analytic functions. Moreover, we compute Bohr and Rogosinski’s radius for poly-analytic functions with analytic counterparts in the class <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <m:mrow> <m:mi>ℱ</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mi>ψ</m:mi> <m:mo>)</m:mo> </m:mrow> </m:mrow> </m:math> or classes of Ma-Minda starlike and convex functions.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135607185","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}
ABSTRACT The purpose of this paper is to find coefficient estimates for the class of functions ℳN(γ,ϑ,λ) consisting of analytic functions f normalized by f (0) = f′ (0) – 1 = 0 in the open unit disk D subordinated to a function generated using the van der Pol numbers, and to derive certain coefficient estimates for a 2 , a 3 , and the Fekete-Szegő functional upper bound for f∈ℳN(γ,ϑ,λ) . Similar results were obtained for the logarithmic coefficients of these functions. Further application of our results to certain functions defined by convolution products with a normalized analytic functions is given, and in particular, we obtain Fekete-Szegő inequalities for certain subclasses of functions defined through the Poisson distribution series.
{"title":"Initial Coefficients and Fekete-Szegő Inequalities for Functions Related to van der Pol Numbers (VPN)","authors":"Gangadharan Murugusundaramoorthy, Teodor Bulboacă","doi":"10.1515/ms-2023-0087","DOIUrl":"https://doi.org/10.1515/ms-2023-0087","url":null,"abstract":"ABSTRACT The purpose of this paper is to find coefficient estimates for the class of functions <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <m:mrow> <m:msub> <m:mi>ℳ</m:mi> <m:mi mathvariant=\"fraktur\">N</m:mi> </m:msub> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>γ</m:mi> <m:mo>,</m:mo> <m:mi>ϑ</m:mi> <m:mo>,</m:mo> <m:mo>λ</m:mo> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:mrow> </m:math> consisting of analytic functions f normalized by f (0) = f′ (0) – 1 = 0 in the open unit disk <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <m:mi mathvariant=\"double-struck\">D</m:mi> </m:math> subordinated to a function generated using the van der Pol numbers, and to derive certain coefficient estimates for a 2 , a 3 , and the Fekete-Szegő functional upper bound for <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"> <m:mrow> <m:mi>f</m:mi> <m:mo>∈</m:mo> <m:msub> <m:mi>ℳ</m:mi> <m:mi mathvariant=\"fraktur\">N</m:mi> </m:msub> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>γ</m:mi> <m:mo>,</m:mo> <m:mi>ϑ</m:mi> <m:mo>,</m:mo> <m:mo>λ</m:mo> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:mrow> </m:math> . Similar results were obtained for the logarithmic coefficients of these functions. Further application of our results to certain functions defined by convolution products with a normalized analytic functions is given, and in particular, we obtain Fekete-Szegő inequalities for certain subclasses of functions defined through the Poisson distribution series.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135607195","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}
ABSTRACT In this paper new oscillatory criteria for odd order linear functional differential equations of the type y(n)(t)+p(t)y(τ(t))=0 [{{y}^{(n)}}(t)+p(t)y(tau (t))=0] have been established. Deviating argument τ(t) is supposed to have dominating delay part.
{"title":"Oscillation of Odd Order Linear Differential Equations with Deviating Arguments with Dominating Delay Part","authors":"B. Baculíková","doi":"10.1515/ms-2023-0070","DOIUrl":"https://doi.org/10.1515/ms-2023-0070","url":null,"abstract":"ABSTRACT In this paper new oscillatory criteria for odd order linear functional differential equations of the type y(n)(t)+p(t)y(τ(t))=0 [{{y}^{(n)}}(t)+p(t)y(tau (t))=0] have been established. Deviating argument τ(t) is supposed to have dominating delay part.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"73 1","pages":"949 - 956"},"PeriodicalIF":1.6,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47638283","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}
ABSTRACT We prove a lower bound estimate for Hajłasz-Besov capacity in metric spaces in terms of Netrusov-Hausdorff content. We also prove a similar estimate for Hajłasz-Triebel-Lizorkin capacity in terms of Hausdoroff content. These results are improvements of the earlier results obtained by Nuutinen in 2016 and the first author in 2020.
{"title":"Besov and Triebel-Lizorkin Capacity in Metric Spaces","authors":"Nijjwal Karak, Debarati Mondal","doi":"10.1515/ms-2023-0069","DOIUrl":"https://doi.org/10.1515/ms-2023-0069","url":null,"abstract":"ABSTRACT We prove a lower bound estimate for Hajłasz-Besov capacity in metric spaces in terms of Netrusov-Hausdorff content. We also prove a similar estimate for Hajłasz-Triebel-Lizorkin capacity in terms of Hausdoroff content. These results are improvements of the earlier results obtained by Nuutinen in 2016 and the first author in 2020.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"73 1","pages":"937 - 948"},"PeriodicalIF":1.6,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46066723","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：