Titlebook: Handbook of Functional Equations; Functional Inequalit Themistocles M. Rassias Book 2014 Springer Science+Business Media, LLC 2014 Cauchy e

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,On a Relation Between the Hardy–Hilbert and Gabriel Inequalities,quality. As an application, we obtain a sharper form of the general Hardy-Hilbert inequality. The integral analogues of our main results are also given. Some Gabriel-type inequalities are also considered.

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Multiplicative Ostrowski and Trapezoid Inequalities,an in the following sense:.We consider the cases of absolutely continuous and logarithmic convex functions. We apply these inequalities to provide approximations for the integral of .; and the first moment of . around zero, that is, .; for an absolutely continuous function . on [.].

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Invariance in the Family of Weighted Gini Means, method of series expansion of means to determine the complementary with respect to a weighted Gini mean. The invariance in the family of weighted Gini means is also studied. The computer algebra Maple was used for solving some complicated systems of equations.

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Comparisons of Means and Related Functional Inequalities,s in this field which according to the best of author’s knowledge remain open. Last section of this paper is devoted to a new, more general functional inequality and a joint generalization of several earlier results is obtained.

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