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A sharp bound for a sine polynomial

Horst Alzer, Stamatis Koumandos (2003)

Colloquium Mathematicae

We prove that | ∑ k = 1 n s i n ( ( 2 k - 1 ) x ) / k | < S i ( π ) = 1 . 8519 . . . for all integers n ≥ 1 and real numbers x. The upper bound Si(π) is best possible. This result refines inequalities due to Fejér (1910) and Lenz (1951).

A sharp companion of Ostrowski’s inequality for the Riemann–Stieltjes integral and applications

Mohammad W. Alomari (2016)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

A sharp companion of Ostrowski’s inequality for the Riemann-Stieltjes integral [...] ∫abf(t) du(t) ∫ a b f ( t ) d u ( t ) , where f is assumed to be of r-H-Hölder type on [a, b] and u is of bounded variation on [a, b], is proved. Applications to the approximation problem of the Riemann-Stieltjes integral in terms of Riemann-Stieltjes sums are also pointed out.

A sharp rearrangement inequality for the fractional maximal operator

A. Cianchi, R. Kerman, B. Opic, L. Pick (2000)

Studia Mathematica

We prove a sharp pointwise estimate of the nonincreasing rearrangement of the fractional maximal function of ⨍, M γ ⨍ , by an expression involving the nonincreasing rearrangement of ⨍. This estimate is used to obtain necessary and sufficient conditions for the boundedness of M γ between classical Lorentz spaces.

A sharp weighted Wirtinger inequality

Tonia Ricciardi (2005)

Bollettino dell'Unione Matematica Italiana

We obtain a sharp estimate for the best constant C > 0 in the Wirtinger type inequality ∫ 0 2 ⁢ π γ p ⁢ ω 2 ≤ C ⁢ ∫ 0 2 ⁢ π γ q ⁢ ω ′ 2 where γ is bounded above and below away from zero, w is 2 ⁢ π -periodic and such that ∫ 0 2 ⁢ π γ p ⁢ ω = 0 , and p + q ≥ 0 . Our result generalizes an inequality of Piccinini and Spagnolo.

Currently displaying 161 – 180 of 297