Extension of Reverse Hilbert-Type Inequality with a Generalized Homogeneous Kernel
Keywords:
Hilbert-Type Integral Inequality, Reverse Hölder's Inequality (es)Downloads
1National University of Mongolia, Ulaanbaatar, Mongolia. Email:tsbatbold@hotmail.com
2National University of Mongolia, Ulaanbaatar, Mongolia. Email:V_Adiyasuren@yahoo.com
3Universidad Nacional de Colombia, Bogotá, Colombia. Email:recastillo@unal.edu.co
In this paper, by introducing some parameters we establish a new extension of the reverse of Hilbert-type integral inequality with best constant. We also, consider the equivalent inequality.
Key words: Hilbert-Type Integral Inequality, Reverse Hölder's Inequality.
2000 Mathematics Subject Classification: 26D15.
En este artículo, introduciendo algunos parámetros, establecemos una nueva extensión de la desigualdad inversa tipo Hilbert con mejor constante. También consideramos la desigualdad equivalente.
Palabras clave: Desigualdad integral tipo Hilbert, desigualdad inversa de Hölder.
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References
[1] G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge University Press, Cambridge, United Kingdom YEAR 1952, 0000.
[2] B. He, `A Reverse Hilbert-Type Inequality with a Generalized Homogeneous Kernel´, Tamkang J. Math 42, 1 (2011), 1-7.
[3] D. S. Mitrinovi\'c, J. E. Pe\vcari\'c, and A. M. Fink, Inequalities Involving Function and Their Integrals and Derivatives, Kluwer Acadamic Publishers, Boston, United States YEAR 1991, 0000.
[4] B. Yang, `A basic Hilbert-Type Integral Inequality with Homogeneous Kernel of -1-Degree´, Journal of Shanghai University (Natural Science) 15, 5 (2009), 493-495.
[5] B. Yang, `A Hilbert-Type Integral Inequality with the Homogeneous Kernel of Degree Zero´, Journal of Shandong University (Natural Science) 45, 2 (2010), 103-106.
Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCMv45n2a07,AUTHOR = {Tserendorj, Batbold and Vandanjav, Adiyasuren and Castillo, René Erlin},
TITLE = {{Extension of Reverse Hilbert-Type Inequality with a Generalized Homogeneous Kernel}},
JOURNAL = {Revista Colombiana de Matemáticas},
YEAR = {2011},
volume = {45},
number = {2},
pages = {187--195}
}
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