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.
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...
We give a Riemann-type definition of the double Denjoy integral of Chelidze and Djvarsheishvili using the new concept of filtering.
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.
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.
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].