On an open problem of integral inequalities.
On an open problem posed in the paper “Inequalities of power-exponential functions".
On an open problem regarding an integral inequality.
On an open question regarding an integral inequality.
On an upper bound for Jensen's inequality.
On an upper bound for the deviations from the mean value.
On approximate Dini derivates and one-sided approximate derivatives of arbitrary functions
On approximate symmetric derivative
On approximation of Baire functions by Darboux functions
On Approximation of the Riemann-Stieltjes Integral and Applications
On - associated comonotone functions
We give a positive answer to two open problems stated by Boczek and Kaluszka in their paper [1]. The first one deals with an algebraic characterization of comonotonicity. We show that the class of binary operations solving this problem contains any strictly monotone right-continuous operation. More precisely, the comonotonicity of functions is equivalent not only to -associatedness of functions (as proved by Boczek and Kaluszka), but also to their -associatedness with being an arbitrary strictly...
On Aumann's theorem that the circle does not admit a mean
On belated differentiation and a characterization of Henstock-Kurzweil-Ito integrable processes
The Henstock-Kurzweil approach, also known as the generalized Riemann approach, has been successful in giving an alternative definition to the classical Itô integral. The Riemann approach is well-known for its directness in defining integrals. In this note we will prove the Fundamental Theorem for the Henstock-Kurzweil-Itô integral, thereby providing a characterization of Henstock-Kurzweil-Itô integrable stochastic processes in terms of their primitive processes.
On Bellman-Bihari integral inequalities.
On best extensions of Hardy-Hilbert's inequality with two parameters.
On Bicheng[Yang]-Debnath's generalizations of Hardy's integral inequality.
On Boman's theorem on partial regularity of mappings
Let and be a positive integer. Let be a locally bounded map such that for each , the derivatives , , exist and are continuous. In order to conclude that any such map is necessarily of class it is necessary and sufficient that be not contained in the zero-set of a nonzero homogenous polynomial which is linear in and homogeneous of degree in . This generalizes a result of J. Boman for the case . The statement and the proof of a theorem of Boman for the case is also extended...
On Borel Classes of Sets of Fréchet Subdifferentiability
We study possible Borel classes of sets of Fréchet subdifferentiability of continuous functions on reflexive spaces.
On Borsík's problem concerning quasiuniform limits of Darboux quasicontinuous functions
On boundedness and discontinuity of additive functions