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

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Functional Inequalities and Analysis of Contagion in the Financial Networks,red. In this paper, considering the Lagrange dual formulation of the financial model, the Lagrange variables called “deficit” and “surplus” variables are considered. By means of these variables, we study the possible insolvencies related to the financial instruments and their propagation to the entire system, producing a “financial contagion”.

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,Inequalities for the Fisher’s Information Measures,e Fisher’s information measure. This generalized (entropy type) Fisher’s information is also discussed as well as the generalized entropy power, while the γ-GND heavily contributes to these generalizations. The appropriate bounds and inequalities of these measures are also provided.

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On Strongly Convex Functions and Related Classes of Functions, A representation of strongly Wright-convex functions and a characterization of functions generating strongly Schur-convex sums are presented. Strongly .-convex and Jensen .-convex functions are investigated. Finally, a relationship between strong convexity and generalized convexity in the sense of Beckenbach is established.

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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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