Classes of Nonnegative Sine Polynomials

Horst Alzer () and Man Kam Kwong ()
Additional contact information
Man Kam Kwong: The Hong Kong Polytechnic University, Department of Applied Mathematics

A chapter in Trigonometric Sums and Their Applications, 2020, pp 71-84 from Springer

Abstract: Abstract We present several one-parameter classes of nonnegative sine polynomials. One of our theorems states that the inequality 0 ≤ ∑ k = 1 n ( 1 n + 1 k ) ( n − k + α ) sin ( k x ) ( α ∈ ℝ ) $$\displaystyle 0\leq \sum _{k=1}^n \Bigl (\frac {1}{n}+\frac {1}{k}\Bigr )(n-k+\alpha )\sin {}(kx) \quad {(\alpha \in \mathbb {R})} $$ 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; 26D05 (search for similar items in EconPapers)
Date: 2020
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-37904-9_3

Ordering information: This item can be ordered from
http://www.springer.com/9783030379049

DOI: 10.1007/978-3-030-37904-9_3

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().