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.
A step to Kurzweil-Henstock—an outline
A short approach to the Kurzweil-Henstock integral is outlined, based on approximating a real function on a compact interval by suitable step-functions, and using filterbase convergence to define the integral. The properties of the integral are then easy to establish.
A stochastic Gronwall inequality and its applications.
A strong boundedness result for separable Rosenthal compacta
It is proved that the class of separable Rosenthal compacta on the Cantor set having a uniformly bounded dense sequence of continuous functions is strongly bounded.
A strongly nonlinear problem arising in glaciology
The computation of glacier movements leads to a system of nonlinear partial differential equations. The existence and uniqueness of a weak solution is established by using the calculus of variations. A discretization by the finite element method is done. The solution of the discrete problem is proved to be convergent to the exact solution. A first simple numerical algorithm is proposed and its convergence numerically studied.
A study of -Laguerre polynomials through the -operator
The present paper deals with certain generating functions and recurrence relations for -Laguerre polynomials through the use of the -operator introduced in an earlier paper [7].
A study of some constants characterizing the weighted Hardy inequality
A study on some new types of Hardy-Hilbert's integral inequality.
A subset of metric preserving functions.
A sufficient condition for the integral version of Martins' inequality.
A supplement to the paper "Differentiable roads for real functions" by J. G. Ceder
A survey of recent reverses for the generalised triangle inequality in inner product spaces