Theorems · Theorem · real analysis
UniformConvexOn.strictConvexOn
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {φ : ℝ → ℝ} {s : Set E} {f : E → ℝ},
UniformConvexOn s φ f → (∀ (r : ℝ), r ≠ 0 → 0 < φ r) → StrictConvexOn ℝ s f- Defined in
- Mathlib.Analysis.Convex.Strong
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Norm.normproof · cited by 5,413
- LT.lt.leproof · cited by 2,189
- LT.lt.ne'proof · cited by 1,417
- LE.le.trans_ltproof · cited by 795
- mul_posproof · cited by 374
- norm_pos_iffproof · cited by 168
- sub_ne_zeroproof · cited by 119
- StrictConvexOnstatement · cited by 84
Cited by1
Results whose statement or proof uses this declaration.
- StrongConvexOn.strictConvexOnproof · cited by 0