Theorems · Theorem · real analysis
Even.strictConvexOn_pow
∀ {n : ℕ}, Even n → n ≠ 0 → StrictConvexOn ℝ Set.univ fun x => x ^ nx^n, n : ℕ is strictly convex on the whole real line whenever n ≠ 0 is even.
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- Foundations
- Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Set.univstatement · cited by 3,945
- StrictMonoproof · cited by 706
- Evenstatement and proof · cited by 444
- Nat.cast_posproof · cited by 113
- StrictConvexOnstatement · cited by 84
- continuous_powproof · cited by 15
- Nat.odd_iffproof · cited by 14
- Odd.strictMono_powproof · cited by 7
- deriv_pow_fieldproof · cited by 3
- Nat.Even.sub_oddproof · cited by 3
- StrictMono.const_mulproof · cited by 2
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