A remark on -systems in groups
A remark on th-order linear functional equations with constant coefficients.
A Remark on the Functional Equation ... (xi) = ....
A representation theorem for entropies with the branching property.
A reversed Poincaré inequality for monotone functions.
A review of selected topics in majorization theory
In this expository paper, some recent developments in majorization theory are reviewed. Selected topics on group majorizations, group-induced cone orderings, Eaton triples, normal decomposition systems and similarly separable vectors are discussed. Special attention is devoted to majorization inequalities. A unified approach is presented for proving majorization relations for eigenvalues and singular values of matrices. Some methods based on the Chebyshev functional and similarly separable vectors...
A role of the coefficient of the differential term in qualitative theory of half-linear equations
The aim of this contribution is to study the role of the coefficient in the qualitative theory of the equation , where with . We discuss sign and smoothness conditions posed on , (non)availability of some transformations, and mainly we show how the behavior of , along with the behavior of the graininess of the time scale, affect some comparison results and (non)oscillation criteria. At the same time we provide a survey of recent results acquired by sophisticated modifications of the Riccati...
A sandwich theorem and Hyers-Ulam stability of affine functions.
A sandwich with convexity.
A separation theorem for -convex functions.
A sharpening of discrete analogues of Wirtinger's inequality
A short proof of the Cushing-Henson conjecture.
A simple functional operator.
A simple system of discrete two-scale difference equations.
A simultaneous system of functional inequalities and mappings which are weakly of a constant sign.
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 solution to a problem of J. Schwaiger.
A special solution of the inhomogeneous Schröder equation.
A stability of the generalized sine functional equations. II.
A stochastic functional equation.