On a trigonometric inequality of Askey and Steinig
Keywords:
rigonometric Inequalities, Dirichlet Kernel
Abstract
A short proof is given for the inequality
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References
[ 1 ] R. Askey, J. Steinig, A Monotonic Trigonometric Sum. Amer. J. Math. 98 (1976), 357-365
[ 2 ] L. Fejer ´ , Lebesguesche Konstanten und divergente Fourierreihen. J. Reine u. Angew. Math. 138 (1910), 22-53
[ 3 ] T.H. Gronwall, Uber die Gibbssche Erscheinung und die trigonometrischen Summen } sin x + 1 2 sin 2x + · · · + n1 sin nx. Math. Ann. 72 (1912), 228-243
[ 4 ] D. Jackson, Uber eine trigonometrische Summe. Rend. Circ. Mat. Palermo } 32 (1911), 257-262
[ 5 ] E. Landau, Uber eine trigonometrische Ungleichung. Math. Z. } 36 (1933), 36
[ 6 ] P. Turan ´ , Uber die partiellen Summen der Fourierreihen. J. London Math. Soc. } 13 (1938), 278-282
[ 7 ] A. Zygmund, Trigonometric Series. Vol. 1,2, Cambridge Univ. Press, 1968.
[ 2 ] L. Fejer ´ , Lebesguesche Konstanten und divergente Fourierreihen. J. Reine u. Angew. Math. 138 (1910), 22-53
[ 3 ] T.H. Gronwall, Uber die Gibbssche Erscheinung und die trigonometrischen Summen } sin x + 1 2 sin 2x + · · · + n1 sin nx. Math. Ann. 72 (1912), 228-243
[ 4 ] D. Jackson, Uber eine trigonometrische Summe. Rend. Circ. Mat. Palermo } 32 (1911), 257-262
[ 5 ] E. Landau, Uber eine trigonometrische Ungleichung. Math. Z. } 36 (1933), 36
[ 6 ] P. Turan ´ , Uber die partiellen Summen der Fourierreihen. J. London Math. Soc. } 13 (1938), 278-282
[ 7 ] A. Zygmund, Trigonometric Series. Vol. 1,2, Cambridge Univ. Press, 1968.
Published
2018-05-31
How to Cite
Helmberg, G. (2018). On a trigonometric inequality of Askey and Steinig. IJRDO -JOURNAL OF MATHEMATICS, 4(5), 01-04. https://doi.org/10.53555/m.v4i5.2006
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Articles
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