An inequality for self reciprocal polynomials
AuthorA. Qazi, Mohammed
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CitationA. Qazi, M. (2019). An inequality for self reciprocal polynomials. International Conference of Mathematical Sciences (ICMS 2019). s. 48.
Let Pn be the class of all polynomials of degree at most n. Polynomials f ∈ Pn which satisfy the condition z nf(1/z) ≡ f(z) are called self-reciprocal and form the sub-class P ∗ n of Pn. For any ρ > 0, let M∞(f ; ρ) := max|z|=ρ |f(z)| and Mp(f ; ρ) := ( 1 2π ∫ π −π |f(ρe iθ )| p dθ )1/p , 0 < p < ∞. If f ∈ Pn then Mp(f ′ ; ρ) ≤ nρn−1 Mp(f ; 1) for any p > 0 and ρ ≥ 1, whereas, if f ∈ P∗ n then Mp(f ′ ; ρ) ≤ (n/2)ρ n−1 Mp(f ; 1) for any p > 0 and ρ ≥ 1. Lately, it has been noted that at least for p ≥ 1, there exists a positive number ρn strictly less than 1 such that Mp(f ′ ; ρ) ≤ nρn−1 Mp(f ; 1) for ρ ≥ ρn if f ∈ Pn. By analogy, it has been asked if there was a positive number ρ ∗ n < 1 such that Mp(f ′ ; ρ) ≤ (n/2)ρ n−1 Mp(f ; 1) for all ρ ≥ ρ ∗ n and any f ∈ P∗ n. We propose to discuss this question.
SourceInternational Conference of Mathematical Sciences (ICMS 2019)
- Makale Koleksiyonu 
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