Webb10 nov. 2024 · Abstract and Figures In this study, we propose a new bound for Jensen's inequality. Under certain conditions, it is an ultimate bound equal to the Jensen gap. To … WebbHowever, applying Jensen on log-sums in Ie and £(XIE» is not as straightforward. Some terms in these expressions involve negative log-sums and so Jensen is actually solving for an upper bound on those terms. If we want overall lower and upper bounds on Ie and £(XIE», we need to compute reverse-Jensen bounds. 5 Reverse-Jensen Bounds

Jensen

WebbFurther sharpening of Jensen's inequality Sang Kyu Lee a Department of Statistics and Probability, Michigan State University, East Lansing, MI, USA View further author … WebbNow, by Jensen’s inequality with weights 1 = = n= 1 n, we have 1 n x 1 p 1 x 1 + x 2 p 1 x 2 + + x n p 1 x n f x 1 + x 2 + + x n n = f 1 n = 1=n p 1 1=n which simpli es to the inequality we wanted. 2.4 The AM-GM inequality The rst example we did can be generalized to a result called the AM-GM (Arithmetic Mean-Geometric Mean) inequality. It ... heart wtf lyrics

Inequalities for $$L^p$$ L p -Norms that Sharpen the Triangle ...

WebbJensen's inequality is an inequality involving convexity of a function. We first make the following definitions: A function is convex on an interval I I if the segment between any two points taken on its graph ( ( in I) I) lies above the graph. An example of a convex function is f (x)=x^2 f (x) = x2. A function is concave on an interval WebbIn particular, just as the Jensen inequality becomes an equality when ϕ is linear, for the new inequality we obtain an equality also when ϕ is quadratic. At the heart of the paper is an apparent new technique for improving classical inequalities based on nonlinear functions. MSC codes analytic function convex function Jensen gap power series WebbThe main aim of this paper is to give an improvement of the recent result on the sharpness of the Jensen inequality. The results given here are obtained using different Green functions and considerin heart wtf