Hardy's and related inequalities in quotients
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Abstract
The main purpose of this paper is to give the well-known Hardy, Polya-Knopp, Hardy-Hilbert, Hardy-Littlewood-Polya and Hilbert-Hardy-type inequalities in quotients. We apply our result on multidimensional setting to obtain new results.
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How to Cite
Iqbal, S., Krulic-Himmelreich, K., & Pečaric, J.
(2014).
Hardy's and related inequalities in quotients.
Acta Mathematica Universitatis Comenianae, 83(2), 195-207.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/87/70
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References
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[2] A. Cizmesija, S. Hussain, J. Pecaric, Some new renement of Hardy and Polya-Knopp's inequalities, Banach. J. Math. Anal. 4 (2010), 122-145.
[3] A. Cizmesija, J. Pecaric, Classical Hardy's and Carleman's inequalities and mixed means, in: T. M. Rassias (ed.), Survey on Classical inequalities, Kluwer Academic Publisher, Dordrecht/ Boston/London, 2000, 27-65.
[4] A. Cizmesija, J. Pecaric, Some new generalizations of the inequalities of Hardy and Levin-Cochran-Lee, Bull. Austral. Math. Soc. 63(1), (2001), 105-113.
[5] A. Cizmesija, J. Pecaric, L.-E. Persson, On strengthened Hardy and Polya-Knopp's inequality, J. Approx. Theory 125, (2003), 74-84.
[6] N. Elezovic, K. Krulic, J. Pecaric, Bounds for Hardy type dierences, Acta Math. Sinica, (Engl. Ser.), 27 (4) (2011), 671-684.
[7] E. K. Godunova, Generalization of a two parameter Hilbert's inequality, (Russian) Izv. Vyss. Ucebn. Zaved. Matematika 1967 54(1) (1967), 35-39.
[8] S. Iqbal, J. Pecaric, Y. Zhou, Generalization of an inequality for integral transforms with kernel and related results, J. Inequal. Appl., vol. 2010. Artical ID 948430, 2010.
[9] S. Iqbal, K. Krulic, J. Pecaric, On an inequality for convex functions with some applications on fractional derivatives and fractional integrals, J. Math. Inequal. 5(2) (2011), 219-230.
[10] S. Kaijser, L-E. Persson, A. Oberg, On Carleman and Knopp's inequalities, J. Approx. Theory 117 (2002), 140-151.
[11] V. Kokilashvili, L.E. Persson, A Meshki, Weighted Norm Inequalities for Integral Transforms with product kernals, Nova Science Publishers, Inc., ISBN 978-1-60741-591-6, New-York, 2009.
[12] K. Krulic, J. Pecaric, L. E. Persson, Some new Hardy type inequalities with general kernels, Math. Inequal. Appl., 12, (2009) 473-485.
[13] A. Kufner, L.-E. Persson, Weighted Inequalities of Hardy Type, World Scientic Publishing Co, Singapore/ New Jersey/ London/Hong Kong, 2003.
[14] J. Pecaric, F. Proschan, Y. L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Inc. 1992.
[2] A. Cizmesija, S. Hussain, J. Pecaric, Some new renement of Hardy and Polya-Knopp's inequalities, Banach. J. Math. Anal. 4 (2010), 122-145.
[3] A. Cizmesija, J. Pecaric, Classical Hardy's and Carleman's inequalities and mixed means, in: T. M. Rassias (ed.), Survey on Classical inequalities, Kluwer Academic Publisher, Dordrecht/ Boston/London, 2000, 27-65.
[4] A. Cizmesija, J. Pecaric, Some new generalizations of the inequalities of Hardy and Levin-Cochran-Lee, Bull. Austral. Math. Soc. 63(1), (2001), 105-113.
[5] A. Cizmesija, J. Pecaric, L.-E. Persson, On strengthened Hardy and Polya-Knopp's inequality, J. Approx. Theory 125, (2003), 74-84.
[6] N. Elezovic, K. Krulic, J. Pecaric, Bounds for Hardy type dierences, Acta Math. Sinica, (Engl. Ser.), 27 (4) (2011), 671-684.
[7] E. K. Godunova, Generalization of a two parameter Hilbert's inequality, (Russian) Izv. Vyss. Ucebn. Zaved. Matematika 1967 54(1) (1967), 35-39.
[8] S. Iqbal, J. Pecaric, Y. Zhou, Generalization of an inequality for integral transforms with kernel and related results, J. Inequal. Appl., vol. 2010. Artical ID 948430, 2010.
[9] S. Iqbal, K. Krulic, J. Pecaric, On an inequality for convex functions with some applications on fractional derivatives and fractional integrals, J. Math. Inequal. 5(2) (2011), 219-230.
[10] S. Kaijser, L-E. Persson, A. Oberg, On Carleman and Knopp's inequalities, J. Approx. Theory 117 (2002), 140-151.
[11] V. Kokilashvili, L.E. Persson, A Meshki, Weighted Norm Inequalities for Integral Transforms with product kernals, Nova Science Publishers, Inc., ISBN 978-1-60741-591-6, New-York, 2009.
[12] K. Krulic, J. Pecaric, L. E. Persson, Some new Hardy type inequalities with general kernels, Math. Inequal. Appl., 12, (2009) 473-485.
[13] A. Kufner, L.-E. Persson, Weighted Inequalities of Hardy Type, World Scientic Publishing Co, Singapore/ New Jersey/ London/Hong Kong, 2003.
[14] J. Pecaric, F. Proschan, Y. L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Inc. 1992.