KnowraEquality conditionLinked fromLinked fromThe 10 pages that link to Equality condition, each with the reason it gives.All 10Broader topic 2Related 8Jensen's inequalityRelated: Strict convexity and identical inputs often determine when Jensen’s bound is tight.Geometric inequalityRelated: The equality configuration often reveals the shape that makes a geometric bound sharp.Minkowski inequalityRelated: Equality in Minkowski depends on alignment of the summands, with details varying by space and exponent.Bernoulli's inequalityRelated: For r>1, equality occurs at x=0 and also at x=−1; endpoint cases depend on r.Nesbitt's inequalityBroader topic: Equality in Nesbitt's inequality holds exactly when all three positive variables are equal.Wirtinger's inequalityRelated: Equality occurs for first-frequency sine and cosine modes and their linear combinations.Young's inequality for productsBroader topic: For positive inputs, equality occurs exactly when a^p = b^q.Shapiro inequalityRelated: Equal variables attain the stated lower bound in the odd cyclic inequality.Barrow's inequalityRelated: It identifies when the vertex-distance sum matches the perpendicular-distance sum.QM–AM–GM–HM inequalitiesRelated: Each adjacent inequality becomes equality exactly when all input numbers are equal.