Extension of Reverse Hilbert-Type Inequality with a Generalized Homogeneous Kernel

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.

Extension of Reverse Hilbert-Type Inequality with a Generalized Homogeneous Kernel Extensión de la desigualdad tipo Hilbert con núcleo homegéneo BATBOLD TSERENDORJ1, ADIYASUREN VANDANJAV2, RENÉ ERLIN CASTILLO3

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 

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Abstract

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.

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2000 Mathematics Subject Classification: 26D15.

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Resumen

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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Texto completo disponible en PDF

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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.

(Recibido en abril de 2011. Aceptado en septiembre de 2011)

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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} 
}