Korean J. Math. Vol. 23 No. 4 (2015) pp.655-664
DOI: https://doi.org/10.11568/kjm.2015.23.4.655

Applications of Taylor series for Carleman's inequality through Hardy inequality

Article Sidebar

PDF
Published: Dec 30, 2015
Keywords:
Hardy inequality, Carleman's inequality, Applications, Taylor series
Mathematics Subject Classification:
26D15

Main Article Content

Mohammed Muniru Iddrisu
Department of Mathematics University for Development Studies, P. O. Box 24, Navrongo campus, Navrongo, Ghana
Christopher Adjei Okpoti
Department of Mathematics University of Education Winneba, Ghana

Abstract

In this paper, we prove the discrete Hardy inequality through the continuous case for decreasing functions using elementary properties of calculus. Also, we prove the Carleman's inequality through limiting the discrete Hardy inequality with applications of Taylor series.


Article Details

References

[1] S. Abramovich, K. Krulic, J. PeVcari c and L.E. Persson, Some new refined Hardy type inequalities with general kernels and measures Aequat. Math. 79 (2010), 157-172. Google Scholar

[2] A. CViVzmeVsija, J. PeVcari c and L.E. Persson, On Strengthened Hardy and Polya- Knopp inequalities J. Approx. Theory 125 (2003), 74-84. Google Scholar

[3] G.H. Hardy, J.E. Littlewood and G. P olya, Inequalities, 2nd ed., Cambridge University Press, Cambridge, (1952) Google Scholar

[4] G.H. Hardy, Note on a theorem of Hilbert, Math. Z. 6, (1920), 314–317. Google Scholar

[5] M. Johansson, L.E. Persson and A. Wedestig, Carleman’s inequality- History, Proofs and Some new generalizations, J. Inequal. Pure Appl. Math. 4 (2003), 1443–5756. Google Scholar

[6] M. Johansson, Carleman type inequalities and Hardy type inequalities for monotone functions, Ph.D thesis, Lule ̊a University of Technology, Sweden, (2007) Google Scholar

[7] S. Kaijser, L. Nikolova, L.E. Persson and A. Wedestig, Hardy-Type Inequalities Via Convexity, J. Math. Ineq. Appl. 8 (2005), 403–417. Google Scholar

[8] S. Kaijser, L. Nikolova, L.E. Persson and A. O ̈berg, On Carleman and Knopp’s Inequalities, J. Approx. Theory 117 (2002), 140–151. Google Scholar

[9] A. Kufner, L. Maligranda and L.E. Persson, The Prehistory of the Hardy Inequality, Amer. Math. Monthly 113 (2006), 715–732. Google Scholar

[10] A. Kufner, L. Maligranda and L.E. Persson, The Hardy inequality: About its History and Some Related Results, Vydavatelsky Sevis Publishing House, Pilsen, (2007) Google Scholar

[11] J.A. Oguntuase and L.E. Persson, Refinement of Hardy inequalities via superquadrattic and subquadratic functions, J. Math. Anal. Appl. 339 (2008), 1305–1312. Google Scholar

[12] J.A. Oguntuase, L.E. Persson, E.K. Essel and B.A. Popoola, Refined multidimensional Hardy-Type Inequalities Via Superquadracity, Banach J. Math. Anal. 2 (2008), 129–139. Google Scholar

[13] C.A. Okpoti, L.E. Persson and A. Wedestig, A Scales of Weight Characterizations for discrete Hardy and Carleman type inequalities, Proc. Function Spaces, Differential Operators and Nonlinear Analysis (FS-DONA 2004), Math. Insti- tute, Acad. Sci., Czech Republic, Milovy, (2004), 236–258. Google Scholar

[14] C.A. Okpoti, Weight characterizations of Discrete Hardy and Carleman’s type inequalities, Ph.D thesis, Lule ̊a University of Technology, Sweden, (2005) Google Scholar

[15] J. PeVcari c and K.B. Stolarsky, Carleman's inequality: History and new generalizations, Aequat. Math. 61 (2001), 49-62. Google Scholar