Linked from

The 23 pages that link to Jensen's inequality, each with the reason it gives.

• Risk aversionRelated: Applied to concave utility, it shows why expected utility favors a sure mean over a risky prospect.

• ConvexityRelated: It generalizes the defining inequality for convex functions to averages.

• Convex combinationRelated: It transfers convexity from points to their convex combinations.

• Geometric inequalityRelated: Convexity converts averages of geometric data into useful bounds.

• Minkowski inequalityRelated: It offers a convexity-based route to related integral norm estimates.

• Expectation–maximization algorithmRelated: It underlies the bound whose successive tightening makes observed-data likelihood nondecreasing.

• AM–GM inequalityRelated: Applied to the logarithm, Jensen's theorem gives a concise modern proof.

• Hermite–Hadamard inequalityRelated: Its general form places Hermite–Hadamard within a broader theory of convex averages.

• Karamata's inequalityRelated: Both inequalities turn convexity into comparisons between averages and sums.

• Popoviciu's inequalityRelated: Convexity is a broader tool for deriving bounds on moments and variance.

• Shapiro inequalityRelated: Convexity can bound transformed expressions arising from the neighboring denominators.

• Carleman's inequalityRelated: The logarithm converts geometric means into averages, linking the inequality to convexity arguments.

• Gibbs' inequalityRelated: Applying it to the logarithm gives a standard proof of Gibbs' inequality.

• Levinson's inequalityRelated: Levinson's result extends the tradition of deriving sum bounds from convexity.

• QM–AM–GM–HM inequalitiesRelated: Convexity of the exponential function yields the arithmetic–geometric mean bound.

• Steffensen's inequalityRelated: It is a foundational classical inequality often used alongside integral bounds.