A Sawyer duality principle for radially monotone functions in .
A selection theorem of Helly type and its applications
We prove an abstract selection theorem for set-valued mappings with compact convex values in a normed space. Some special cases of this result as well as its applications to separation theory and Hyers-Ulam stability of affine functions are also given.
A separation theorem for -convex functions.
A sequence of mappings associated with the Hermite-Hadamard inequalities and applications
New properties for some sequences of functions defined by multiple integrals associated with the Hermite-Hadamard integral inequality for convex functions and some applications are given.
A sequence of mappings connected with Jensen's inequality and applications
A sequence of sharp trigonometric inequalities
A sharp bound for a sine polynomial
We prove that 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 bound of the Čebyšev functional for the Riemann-Stieltjes integral and applications.
A sharp companion of Ostrowski’s inequality for the Riemann–Stieltjes integral and applications
A sharp companion of Ostrowski’s inequality for the Riemann-Stieltjes integral [...] ∫abf(t) du(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 double inequality for sums of powers.
A sharp inequality of Ostrowski-Grüss type.
A sharp rearrangement inequality for the fractional maximal operator
We prove a sharp pointwise estimate of the nonincreasing rearrangement of the fractional maximal function of ⨍, , by an expression involving the nonincreasing rearrangement of ⨍. This estimate is used to obtain necessary and sufficient conditions for the boundedness of between classical Lorentz spaces.
A sharp weighted Wirtinger inequality
We obtain a sharp estimate for the best constant in the Wirtinger type inequality where is bounded above and below away from zero, is -periodic and such that , and . Our result generalizes an inequality of Piccinini and Spagnolo.
A sharpening of discrete analogues of Wirtinger's inequality
A short proof of Ky Fan's inequality
A Sierpiński-Zygmund function which has a perfect road at each point
A simple proof of monotonicity for Stolarsky and Gini means
A simple proof of the Chui-Smith theorem on Landau's problem
A simple proof of the Fundamental Theorem of Algebra
In the paper an elementary and simple proof of the Fundamental Theorem of Algebra is given.
A simple proof of the geometric-arithmetic mean inequality.