Theorems · Theorem · real analysis

StrictConvexOn.secant_strict_mono_aux1

∀ {𝕜 : Type u_1} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜] {s : Set 𝕜} {f : 𝕜 → 𝕜},
  StrictConvexOn 𝕜 s f → ∀ {x y z : 𝕜}, x ∈ s → z ∈ s → x < y → y < z → (z - x) * f y < (z - y) * f x + (y - x) * f z

Defined in

Mathlib.Analysis.Convex.Slope

Cited by

2 results in Mathlib

Foundations

Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRing