On Some Integral Inequalities of Hardy-Type Operators

ABSTRACT

In recent time, hardy integral inequalities have received attentions of many researchers. The aim of this paper is to obtain new integral inequalities of hardy-type which complement some recent results.

Cite this paper

R. Kamilu, O. Olorunju and S. Akeem, "On Some Integral Inequalities of Hardy-Type Operators,"*Advances in Pure Mathematics*, Vol. 3 No. 7, 2013, pp. 609-614. doi: 10.4236/apm.2013.37078.

R. Kamilu, O. Olorunju and S. Akeem, "On Some Integral Inequalities of Hardy-Type Operators,"

References

[1] G. H. Hardy, “Notes on a Theorem of HILBERT,” Mathematische Zeltschrift, Vol. 6, 1920, pp. 314-317.

[2] R. A. Adams, “Sobolev Spaces,” Academic Press, New York-London, 1975.

[3] G. H. Hardy, J. E. Littlewood and G. Polya, “Inequalities,” Cambridge University Press, Cambridge, 1952, MR0046395(13:727e), Reprinted 1991.

[4] A. Kufner and L.-E. Persson, “Weighted Inequalities of Hardy Type,” The American Mathematical Monthly, World Scientific, New Jersey, London, Singapore, Hong Kong, 2003. http://dx.doi.org/10.1142/5129

[5] A. Kufner, L. Maligranda and L.-E. Persson, “The Hardy Inequality—About Its History and Some Related Results,” Vydavatelsky Servis Publishing House, Pilsen, 2007.

[6] C. P. Niculescu and L.-E. Persson, “Convex Functions and Their Applications. A Contemporary Approach,” Springer, Berlin, Heidelberg, New York, Hong Kong, London, Milan, Paris, Tokyo, 2005.

[7] B. Opic and A. Kufner, “Hardy Type Inequalities,” Longman, Harlow, 1990.

[8] K. Rauf, J. O. Omolehin and J. A. Gbadeyan, “On Some Refinement of Results on Hardy’s Integral Inequality,” International Journal of Scientific Computing, Vol. 1, No. 1, 2007, pp. 15-20.

[9] Y. Bicheng, Z. Zhuohua and L. Debnath, “Note on New Generalizations of Hardy’s Integral Inequality,” Journal of Mathematical Analysis and Applications, Vol. 217, No. 1, 1998, pp. 321-327.

http://dx.doi.org/10.1006/jmaa.1998.5758

[10] A. G. Adeagbo-Sheikh and C. O. Imoru, “An Integral Inequality of the Hardy’s Type,” Kragujevac Journal of Mathematics, Vol. 29, 2006, pp. 57-61.

[11] S. S. Dragomir and N. M. Ionescu, “Some Converse of Jensen’s Inequality and Applications,” Revue d'Analyse Numérique et de Théorie de l’Approximation, Vol. 23, No. 1, 1994, pp. 71-78.

[12] C. O. Imoru and A. G. Adeagbo-Sheikh, “On Some Weighted Mixed Norm Hardy-Type Integral Inequalities,” Journal of Inequalities in Pure and Applied Mathamatics, Vol. 8, No. 4, 2007, pp. 1-12.

[13] S. Kaijser, L. Nikolova, L.-E. Persson and A. Wedestig, “Hardy-Type Inequalities via Convexity,” Mathematical Inequalities & Applications, Vol. 8, No. 3, 2005, pp. 403-417.

[14] K. Rauf and J. O. Omolehin, “Some Notes on an Integral Inequality Related to G.H. Hardy’s Integral Inequality,” Punjab University Journal of Mathematics, Vol. 38, 2006, pp. 9-13.

[15] M. Z. Sarkaya and H. Yildirim, “Some Hardy Type Integral Inequalities,” Journal of Inequalities in Pure and Applied Mathematics, Vol. 7, No. 5, 2006, pp. 1-5.

[16] L. Zhongxue, G. Mingzhe and L. Debnath, “On New Generalizations of the Hilbert Integral Inequality,” Journal of Mathematical Analysis and Applications, Vol. 326, No. 2, 2007, pp. 1452-1457.

http://dx.doi.org/10.1016/j.jmaa.2006.03.039

[1] G. H. Hardy, “Notes on a Theorem of HILBERT,” Mathematische Zeltschrift, Vol. 6, 1920, pp. 314-317.

[2] R. A. Adams, “Sobolev Spaces,” Academic Press, New York-London, 1975.

[3] G. H. Hardy, J. E. Littlewood and G. Polya, “Inequalities,” Cambridge University Press, Cambridge, 1952, MR0046395(13:727e), Reprinted 1991.

[4] A. Kufner and L.-E. Persson, “Weighted Inequalities of Hardy Type,” The American Mathematical Monthly, World Scientific, New Jersey, London, Singapore, Hong Kong, 2003. http://dx.doi.org/10.1142/5129

[5] A. Kufner, L. Maligranda and L.-E. Persson, “The Hardy Inequality—About Its History and Some Related Results,” Vydavatelsky Servis Publishing House, Pilsen, 2007.

[6] C. P. Niculescu and L.-E. Persson, “Convex Functions and Their Applications. A Contemporary Approach,” Springer, Berlin, Heidelberg, New York, Hong Kong, London, Milan, Paris, Tokyo, 2005.

[7] B. Opic and A. Kufner, “Hardy Type Inequalities,” Longman, Harlow, 1990.

[8] K. Rauf, J. O. Omolehin and J. A. Gbadeyan, “On Some Refinement of Results on Hardy’s Integral Inequality,” International Journal of Scientific Computing, Vol. 1, No. 1, 2007, pp. 15-20.

[9] Y. Bicheng, Z. Zhuohua and L. Debnath, “Note on New Generalizations of Hardy’s Integral Inequality,” Journal of Mathematical Analysis and Applications, Vol. 217, No. 1, 1998, pp. 321-327.

http://dx.doi.org/10.1006/jmaa.1998.5758

[10] A. G. Adeagbo-Sheikh and C. O. Imoru, “An Integral Inequality of the Hardy’s Type,” Kragujevac Journal of Mathematics, Vol. 29, 2006, pp. 57-61.

[11] S. S. Dragomir and N. M. Ionescu, “Some Converse of Jensen’s Inequality and Applications,” Revue d'Analyse Numérique et de Théorie de l’Approximation, Vol. 23, No. 1, 1994, pp. 71-78.

[12] C. O. Imoru and A. G. Adeagbo-Sheikh, “On Some Weighted Mixed Norm Hardy-Type Integral Inequalities,” Journal of Inequalities in Pure and Applied Mathamatics, Vol. 8, No. 4, 2007, pp. 1-12.

[13] S. Kaijser, L. Nikolova, L.-E. Persson and A. Wedestig, “Hardy-Type Inequalities via Convexity,” Mathematical Inequalities & Applications, Vol. 8, No. 3, 2005, pp. 403-417.

[14] K. Rauf and J. O. Omolehin, “Some Notes on an Integral Inequality Related to G.H. Hardy’s Integral Inequality,” Punjab University Journal of Mathematics, Vol. 38, 2006, pp. 9-13.

[15] M. Z. Sarkaya and H. Yildirim, “Some Hardy Type Integral Inequalities,” Journal of Inequalities in Pure and Applied Mathematics, Vol. 7, No. 5, 2006, pp. 1-5.

[16] L. Zhongxue, G. Mingzhe and L. Debnath, “On New Generalizations of the Hilbert Integral Inequality,” Journal of Mathematical Analysis and Applications, Vol. 326, No. 2, 2007, pp. 1452-1457.

http://dx.doi.org/10.1016/j.jmaa.2006.03.039