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Classes of Nonnegative Sine Polynomials

  • Horst AlzerEmail author
  • Man Kam Kwong
Chapter
  • 65 Downloads

Abstract

We present several one-parameter classes of nonnegative sine polynomials. One of our theorems states that the inequality
$$\displaystyle 0\leq \sum _{k=1}^n \Bigl (\frac {1}{n}+\frac {1}{k}\Bigr )(n-k+\alpha )\sin {}(kx) \quad {(\alpha \in \mathbb {R})} $$
holds for all n ≥ 1 and x ∈ [0, π] if and only if α ∈ [0, 3]. This extends a result of Dimitrov and Merlo (2002), who proved the inequality for α = 1.

Keywords

Sine polynomials Inequalities 

2010 Mathematics Subject Classification

26D05 

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.WaldbrölGermany
  2. 2.Department of Applied MathematicsThe Hong Kong Polytechnic UniversityHong KongChina

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