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3 results

  • SOME REVERSES OF THE JENSEN INEQUALITY WITH APPLICATIONS

  • S. S. DRAGOMIR
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 87 / Issue 2 / April 2013
    Published online by Cambridge University Press:
    07 February 2013, pp. 177-194
    Print publication:
    April 2013
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  • Two new reverses of the celebrated Jensen’s inequality for convex functions in the general setting of the Lebesgue integral, with applications to means, Hölder’s inequality and $f$-divergence measures in information theory, are given.

  • INEQUALITIES IN TERMS OF THE GÂTEAUX DERIVATIVES FOR CONVEX FUNCTIONS ON LINEAR SPACES WITH APPLICATIONS

  • Part of
  • S. S. DRAGOMIR
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 83 / Issue 3 / June 2011
    Published online by Cambridge University Press:
    07 February 2011, pp. 500-517
    Print publication:
    June 2011
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  • Some inequalities in terms of the Gâteaux derivatives related to Jensen’s inequality for convex functions defined on linear spaces are given. Applications for norms, mean f-deviations and f-divergence measures are provided as well.

  • BOUNDS FOR THE DEVIATION OF A FUNCTION FROM THE CHORD GENERATED BY ITS EXTREMITIES

  • Part of
  • S. S. DRAGOMIR
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 78 / Issue 2 / October 2008
    Published online by Cambridge University Press:
    01 October 2008, pp. 225-248
    Print publication:
    October 2008
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  • Sharp bounds for the deviation of a real-valued function f defined on a compact interval [a,b] to the chord generated by its end points (a,f(a)) and (b,f(b)) under various assumptions for f and f′, including absolute continuity, convexity, bounded variation, and monotonicity, are given. Some applications for weighted means and f-divergence measures in information theory are also provided.