数学与计算机科学 |
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一个R2上含双曲函数核的Hilbert型不等式 |
有名辉, 孙霞 |
浙江机电职业技术学院 数学教研室, 浙江 杭州 310053 |
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A Hilbert-type inequality defined on R2 with the kernel involving hyperbolic functions |
YOU Minghui, SUN Xia |
Mathematics Teaching and Research Section, Zhejiang Institute of Mechanical and Electrical Engineering, Hangzhou 310053, China |
1 HARDY G H, LITTLEWOOD J E, POLYA G. Inequalities[M]. London:Cambridge University Press, 1952. 2 杨必成.关于一个Hilbert类积分不等式的推广及应用[J].应用数学,2003,16(2):82-86. YANG B C.On a generalization of a Hilbert’s type integral inequality and its application[J]. Mathematics Applicata,2003,16(2): 82-86. 3 JIN J J. On Hilbert’s type inequalities[J]. Journal of Mathematical Analysis and Applications, 2008, 340(2):932-942. DOI: 10.1016/j.jmaa.2007.09.036 4 MICHAEL T H, ASSIAS R, YANG B C. A Hilbert-type integral inequality in the whole plane related to the hypergeometric function and the beta function[J]. Journal of Mathematical Analysis and Applications, 428(1): 1286-1308. DOI: 10.1016/j.jmaa.2015.04.003 5 KUANG J C, DEBNATH L. On new generalizations of Hilbert’s inequality and their applications[J].Journal of Mathematical Analysis and Applications, 2000, 245(1):248-265. DOI: 10.1006/jmaa.2000.6766 6 YOU M H.On a new discrete Hilbert-type inequality and its application[J]. Mathematical Inequalities & Applications, 2015,18 (4): 1575-1587. 7 有名辉. 一个与 Euler数有关的Hilbert型不等式的推广[J]. 浙江大学学报(理学版), 2016,43(2) :144-148. DOI:10.3785/j.issn.1008-9497.2016.02.004 YOU M H. Generalization of a Hilbert-type inequality related to Euler number[J].Journal of Zhejiang University(Science Edition), 2016,43(2):144-148. DOI:10.3785/j.issn.1008-9497.2016.02.004 8 杨必成. 算子范数与Hilbert型不等式[M]. 北京: 科学出版社, 2009. YANG B C.The Norm of Operator and Hilbert-Type Inequalities[M]. Beijing: Science Press, 2009. 9 KRNIĆ M, PEČARIĆ J, PERIĆ I, et al. Recent Advances in Hilbert-Type Inequalities[M]. Zagreb: Element Press, 2012. 10 MINTRINOVIC D S, PECARIC J E, FINK M. Inequalities Involving Functions and Their Integrals and Derivatives[M]. Boston: Kluwer Academic Press, 1991. 11 刘琼,龙顺潮. 一个核为双曲余割函数的Hilbert型积分不等式[J].数学学报(中文版),2013,56(1):97-104. LIU Q, LONG S C. A new Hilbert-type integral inequality with the kernel of hyperbolic cosecant function[J]. Acta Mathematica Sinica (Chinese Series), 2013, 56(1): 97-104. 12 LIU Q. A Hilbert-type integral inequality with the mixed kernel and its applications [J]. Mathematica Applicata, 2015, 28(3):567-573. DOI: 10.4064/cm6572-1-2016 13 LIU Q, SUN W. A Hilbert-type integral inequality with the mixed kernel of multi-parameters [J]. Comptes Rendus Mathematique, 2013, 351(15): 605-611. DOI: 10.1016/j.crma.2013.09.001. 14 杨必成,陈强. 一个核为双曲正割函数的半离散Hilbert型不等式[J]. 西南师范大学学报(自然科学版), 2015,40(2) :26-32. DOI: 10.13718/j.cnki.xsxb.2015.02.006 YANG B C, CHEN Q.On a half-discrete Hilbert-type inequality with kernel related to hyperbolic secant function[J].Journal of Southwest China Normal University (Natural Science Edition), 2015,40(2) :26-32. DOI: 10.13718/j.cnki.xsxb.2015.02.006 15 菲赫金哥尔茨 ΓM. 微积分学教程(第2卷)[M]. 徐献瑜,冷生明,梁文琪译.北京:高等教育出版社,2006:695,397. FIKHTENGOLTS ΓM. Calculus Course (Volume Second)[M].Translated by XU X Y,LENG S M,LIANG W Q. Beijing:Higher Education Press, 2006:695,397. 16 匡继昌. 常用不等式[M].第3版. 济南:山东科学技术出版社,2010:5. KUANG J C. Applied Inequalities [M].3rd ed. Jinan:Shandong Science and Technology Press, 2010:5. |
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