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- W86929498 abstract "We introduce the multiplicative Ostrowski and trapezoid inequalities, that is, providing bounds for the comparison of a function f and its integral mean in the following sense: $$begin{aligned} f(x) {rm exp}! left[!-frac{1}{b-a}int_a^b!! log f(t), dt!right]! text{and}! f(b)^{frac{b-x}{b-a}} f(a)^{frac{x-a}{b-a}} {rm exp}! left[!-frac{1}{b-a}int_a^b!! log f(t), dt!right].end{aligned}$$ We consider the cases of absolutely continuous and logarithmic convex functions. We apply these inequalities to provide approximations for the integral of f; and the first moment of f around zero, that is, $int_{a}^{b}xf(x)dx$ ; for an absolutely continuous function f on [ $a,b$ ]." @default.
- W86929498 created "2016-06-24" @default.
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- W86929498 date "2014-01-01" @default.
- W86929498 modified "2023-09-23" @default.
- W86929498 title "Multiplicative Ostrowski and Trapezoid Inequalities" @default.
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- W86929498 doi "https://doi.org/10.1007/978-1-4939-1246-9_4" @default.
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