A relaxation result in BV for integral functionals with discontinuous integrands
We prove a relaxation theorem in BV for a non coercive functional with linear growth. No continuity of the integrand with respect to the spatial variable is assumed.
A remark on functions continuous on all lines
We prove that each linearly continuous function on (i.e., each function continuous on all lines) belongs to the first Baire class, which answers a problem formulated by K. C. Ciesielski and D. Miller (2016). The same result holds also for on an arbitrary Banach space , if has moreover the Baire property. We also prove (extending a known finite-dimensional result) that such on a separable is continuous at all points outside a first category set which is also null in any usual sense.
A remark on generalized iterates.
A remark on -harmonic functions on Riemannian manifolds.
A remark on linear functions on the sphere
A remark on local fractional calculus and ordinary derivatives
In this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new concept and ordinary differentiation. Using such formula, most of the fundamental properties of the fractional derivative can be derived directly.
A remark on the compactness for the Cahn–Hilliard functional
In this note we prove compactness for the Cahn–Hilliard functional without assuming coercivity of the multi-well potential.
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.