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

TSERENDORJ, BATBOLD; VANDANJAV, ADIYASUREN; CASTILLO, RENÉ ERLIN

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Revista Colombiana de Matemáticas

Print version ISSN 0034-7426

Rev.colomb.mat. vol.45 no.2 Bogotá July/Dec. 2011

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

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.

2000 Mathematics Subject Classification: 26D15.

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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References

[1] G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge University Press, Cambridge, United Kingdom YEAR 1952, [ Links ] 0000.

[2] B. He, 'A Reverse Hilbert-Type Inequality with a Generalized Homogeneous Kernel', Tamkang J. Math 42, 1 (2011), [ Links ] 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, [ Links ] 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. [ Links ]

[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. [ Links ]

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

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}    
 }