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Indexed by:期刊论文

Date of Publication:2013-06-01

Journal:RESULTS IN MATHEMATICS

Included Journals:SCIE

Volume:63

Issue:3-4

Page Number:1215-1223

ISSN No.: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).