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.
A simple proof of the minimax-theorem
A simple proof of the Poincaré inequality for a large class of probability measures.
A simple proof of the Rademacher theorem
A simplified multidimensional integral
We present a simplified integral of functions of several variables. Although less general than the Riemann integral, most functions of practical interest are still integrable. On the other hand, the basic integral theorems can be obtained more quickly. We also give a characterization of the integrable functions and their primitives.
A simultaneous solution to two problems of derivatives.
A Sobolev-type inequality with applications.
A solution of an open problem concerning Lagrangian mean-type mappings
The problem of invariance of the geometric mean in the class of Lagrangian means was considered in [Głazowska D., Matkowski J., An invariance of geometric mean with respect to Lagrangian means, J. Math. Anal. Appl., 2007, 331(2), 1187–1199], where some necessary conditions for the generators of Lagrangian means have been established. The question if all necessary conditions are also sufficient remained open. In this paper we solve this problem.
A spherical representation of the real directional derivative.
A stability version of Hölder's inequality for .
A Steffensen type inequality.