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Some approximations of the Csiszár f − divergence by the use of Taylor's formula and perturbed Taylor's formula and some applications for Kullback-Leibler distance are given. Mathematics subject classification (2000): 26D15.
Some Ostrowski and trapezoid type inequalities for the Stieltjes integral in the case of Lischitzian integrators for both Hölder continuous and monotoonic integrals are obtained. The dual case is also analysed. Applications for the midpoint rule are pointed out as well.
On utilising an identity from , some weighted Ostrowski type inequalities are established.
A companion for the Ostrowski and the generalised trapezoid in-equalites for various classes of functions, including functions of bounded variation , Lipschitzian, convex and absolutely continuous functions is established. Applications for weighted means are also given.
Utilising the Beesack version of the Darst-Pollard inequality, some error bounds for approximating the Riemann-Stieltjes integral are given. Some applications related to the trapezoid and mid-point quadrature rules are provided .
Inequalities of the majorisation type for convex functions and Stieltjes integrals are given. Applications for some particular convex functions of interest are also pointed out.
An inequality of Ostrowski's type for a random variable whose probability density function is in L p [a, b] , p > 1, in terms of the cumulative distribution function and expectation is given. An application for a Beta random variable is also given.
Some inequalities for the expectation and variance of a random variable whose p.d.f. is n-time differentiable are given.