Several applications of Cartwright-Field's inequality

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Minculete, Nicuşor; Furuichi, Shigeru;
  • Subject: Mathematics - Classical Analysis and ODEs | Mathematics - Functional Analysis

In this paper we present several applications of Cartwright-Field's inequality. Among these we found Young's inequality, Bernoulli's inequality, the inequality between the weighted power means, H\"{o}lder's inequality and Cauchy's inequality. We give also two applicatio... View more
  • References (12)
    12 references, page 1 of 2

    [1] T. M. APOSTOL, Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976.

    [2] D. I. CARTWRIGHT, M. J. FIELD, A refinement of the arithmetic mean-geometric mean inequality, Proc. Amer. Math. Soc., Vol.71(1978), pp.36-38.

    [3] S. FURUICHI, On refined Young inequalities and reverse inequalities, J. Math. Ineq., Vol.5(2011), pp.21-31.

    [4] S. FURUICHI, N. MINCULETE, Alternative reverse inequalities for Young's inequality, arXiv:1103.1937.

    [5] T.FURUTA, M.YANAGIDA, Generalized means and convexity of inversion for positive operators, Amer.Math.Monthly, Vol.105 (1998),pp.258-259.

    [6] G. H. HARDY, J. E. LITLLWOOD, G. POLYA, Inequalities, Cambrige University Press, 1934.

    [7] F. KUBO, T.ANDO, Means of positive operators, Math. Ann.,Vol.264(1980),pp.205-224.

    [8] M. NATHANSON, Elementary Methods in Number Theory, Springer, New York, 2006.

    [9] C. P. NICULESCU, L.-E. PERSSON, Convex Functions and Their Applications, CMS Books in Mathematics, Vol. 23, Springer-Verlag, New York, 2006.

    [10] O. T. POP, About Bergstr¨om's inequality, Journal of Mathematical Inequalities, Vol. 3(2009), pp.213-216.

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