Results 151 to 160 of about 18,466 (195)

Turan's Inequalities for Trigonometric Polynomials

Journal of the London Mathematical Society, 1996
We present a technique for establishing inequalities of the form \[ c |f |_\infty \leq \int^{2 \pi}_0 \varphi \biggl (\bigl |f^{(k)} (t) \bigr |\biggr) dt \leq M |f |_\infty \] in the set of all trigonometric polynomials of order \(n\) which have only real zeros. The function \(\varphi\) is assumed to be convex and increasing on \([0, \infty)\).
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Inequalities for trigonometric polynomials

Approximation Theory and its Applications, 1997
Summary: Let \(t_n(x)\) be any real trigonometric polynomial of degree \(n\) such that \(\| t_n\|_\infty\leq 1\). Here, we are concerned with obtaining the best possible upper estimate of \[ \int^{2\pi}_0 | t^{(k)}_n(x)|^q dx\Biggl/\int^{2\pi}_0| t^{(k)}_n(x)|^{q- 2}dx, \] where \(q>2\).
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Remarks on trigonometric inequalities

1992
We consider expansions of ((sin z)/z)m and ((sin z)/z)m / cos z in powers of sin z, which can be used to generate a sequence of two-sided inequalities for ((sin x)/x)m (m = 1, 2, 3,...).
L. Lorch, D. C. Russell
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Inequalities for Weighted Trigonometric Sums

2020
We prove that the double-inequality $$\displaystyle \left ( \sum _{j=1}^n \frac {w_j}{ 1-\sin ^2 \frac {j\pi }{n+1} } \right )^a \leq \sum _{j=1}^n \frac {w_j}{ 1-\sin \frac {j\pi }{n+1} } \cdot \sum _{j=1}^n \frac {w_j}{ 1+\sin \frac {j\pi }{n+1} } \leq \left ( \sum _{j{=}1}^n \frac {w_j}{ 1{-}\sin ^2 \frac {j\pi }{n{+}1} } \right )^b $$ holds ...
Horst Alzer, Omran Kouba
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Some inequalities in trigonometric approximation

Bulletin of the Australian Mathematical Society, 1973
For a nonconstant L2 (−π, π) function f, we prove that and that the inequalities are sharp.
Ching, Chin-Hung, Chui, Charles K.
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106.10 PWW: Trigonometric inequality

The Mathematical Gazette, 2022
Victor Oxman, Moshe Stupel
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A further note on trigonometrical inequalities

Mathematical Proceedings of the Cambridge Philosophical Society, 1950
1. The aim of this note is to prove theTheorem. Letwhere the λnare real andand letThenA similar result holds for infinite seriesconverging uniformly in [−T, T].
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On Some Trigonometric Functional Inequalities

2002
We deal with d’Alembert’s and Wilson’s differences $$f\left( {x + y} \right) + f\left( {x - y} \right) - 2f\left( x \right)f\left( y \right)$$ and $$f\left( x \right)f\left( y \right) - f{\left( {\frac{{x + y}}{2}} \right)^2} + f{\left( {\frac{{x - y}}{2}} \right)^2}$$ respectively, assuming that their absolute values (or norms) are ...
Roman Badora, Roman Ger
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An Approach to Trigonometric Inequalities

Mathematics Magazine, 1970
(1970). An Approach to Trigonometric Inequalities. Mathematics Magazine: Vol. 43, No. 5, pp. 254-257.
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Integrative oncology: Addressing the global challenges of cancer prevention and treatment

Ca-A Cancer Journal for Clinicians, 2022
Jun J Mao,, Msce, Lorenzo Cohen, Karen M Mustian   +2 more
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