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A refinement of Carleman's inequality

F. Qi|J. Cao, D.-W. Niu
장전수학회 (Jangjeon Mathematical Society)|2006.07|Advanced Studies in Contemporary Mathematics|제13권 제1호|pp. 57-62

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주제분류수학

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Abstract

In this note, the well known Carleman’s inequality is rened byestablishing the upper and lower bounds for the sequence (1 + 1 /n)n .

참고문헌 (12)

  1. Chen, Ch.-P., "Note on weighted Carleman-type inequality", Internat. J. Math. Math. Sci., (3), pp.475~481 (2005)
  2. Ciˆzmeˆsija, A., "On strangthened weighted Carleman’s inequality", Bull. Austral. Math. Soc., 68(3), pp.481~490 (2003)
  3. Hardy, G., "Inequalities" (1952), Cambridge Univ. Press
  4. "Carleman’s inequality—History, proofs and some new generalizations(J. Inequal. Pure Appl. Math. 4 (2003), no. 3, Art 53)" (2009)[URL]
  5. Kufner, A., "Weighted Inequalities of Hardy Type" (2003), World Scientific Publishing,New Jersey
  6. Okpoti, C. A., "Scales of weight characterizations for some multidimensional discrete Hardy and Carleman type inequalities", Proc. A. Razmadze Math. Inst., 138, pp.63~84 (2005)
  7. "Generalized abstracted mean values(J. Inequal. Pure Appl. Math. 1 (2000), no. 1, Art. 4 ; RGMIA Res. Rep. Coll. 2 (1999), no. 5, Art. 4, 633–642)" (2009)[URL]
  8. "The extended mean values: definition, properties, monotonicities, comparison, convexities, generalizations, and applications(Cubo Mat. Educ. 5 (2003), no. 3, 63–90 ; RGMIA Res. Rep. Coll. 5 (2002), no. 1, Art. 5, 57–80)" (2009)[URL]
  9. Yan, P., "A strengthened Carleman’s inequality", J. Math. Anal. Appl., 240(1), pp.290~293 (1999)
  10. Yang, B.-Ch., "Some inequality involving the constant e, and an application to Carleman’s inequality", J. Math. Anal. Appl., 223(1), pp.347~353 (1998)
  11. "A strengthened Carleman’s inequality(RGMIA Res. Rep. Coll. 3 (2000), no. 3, Art. 17)" (2009)[URL]
  12. "Refinements of Carleman’s inequality(J. Inequal. Pure Appl. Math. 2 (2001),no. 2, Art. 21 ; RGMIA Res. Rep. Coll. 3 (2000), no. 3, Art. 8)" (2009)[URL]

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