Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2013-06-01

Journal: RESULTS IN MATHEMATICS

Included Journals: SCIE

Volume: 63

Issue: 3-4

Page Number: 1215-1223

ISSN: 1422-6383

Key Words: Alternating trigonometric sums; inequalities; sharp constant bounds; hypermetric spaces

Abstract: In 1970, J.B. Kelly proved that
   0 <= Sigma(n)(k=1)(-1)(k+1)(n - k + 1)vertical bar sin(kx)vertical bar (n is an element of N; x is an element of R).
   We generalize and complement this inequality. Moreover, we present sharp upper and lower bounds for the related sums
   Sigma(n)(k=1)(-1)(k+1)(n - k + 1)vertical bar cos(kx)vertical bar and
   Sigma(n)(k=1)(-1)(k+1)(n - k + 1)(vertical bar sin(kx)vertical bar + vertical bar cos(kx)vertical bar).