A Remark on the Multidimensional Moment Problem.
A remark over the converse of Hölder inequality.
A Representation Theorem for a Convex Cone of Quasi Convex Functions.
A representation theorem for operators on a space of interval functions.
A reverse Hardy-Hilbert-type inequality.
A reverse Hardy-Hilbert-type integral inequality.
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 Riemann-type definition for the double Denjoy integral of Chelidze and Djvarsheishvili
We give a Riemann-type definition of the double Denjoy integral of Chelidze and Djvarsheishvili using the new concept of filtering.
A roller coaster approach to integration and Peano's existence theorem
This is a didactic proposal on how to introduce the Newton integral in just three or four sessions in elementary courses. Our motivation for this paper were Talvila's work on the continuous primitive integral and Koliha's general approach to the Newton integral. We introduce it independently of any other integration theory, so some basic results require somewhat nonstandard proofs. As an instance, showing that continuous functions on compact intervals are Newton integrable (or, equivalently, that...
A sandwich theorem and Hyers-Ulam stability of affine functions.
A sandwich with convexity.
A sandwich with convexity for set-valued functions.
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).