In a previous paper we defined a Denjoy integral for mappings from a vector lattice to a complete vector lattice. In this paper we define a Henstock-Kurzweil integral for mappings from a vector lattice to a complete vector lattice and consider the relation between these two integrals.
In this paper we define the derivative and the Denjoy integral of mappings from a vector lattice to a complete vector lattice and show the fundamental theorem of calculus.
According to A. Lasota, a continuous function from a real compact interval into itself is called generically chaotic if the set of all points , for which and , is residual in . Being inspired by this definition we say that is densely chaotic if this set is dense in . A characterization of the generically chaotic functions is known. In the paper the densely chaotic functions are characterized and it is proved that in the class of piecewise monotone maps with finite number of pieces the...
We prove that density preserving homeomorphisms form a Π11-complete subset in the Polish space ℍ of all increasing autohomeomorphisms of unit interval.
If E is a Banach space, any element x** in its bidual E** is an affine function on the dual unit ball that might possess a variety of descriptive properties with respect to the weak* topology. We prove several results showing that descriptive properties of x** are quite often determined by the behaviour of x** on the set of extreme points of , generalizing thus results of J. Saint Raymond and F. Jellett. We also prove a result on the relation between Baire classes and intrinsic Baire classes...
Mathematics Subject Classification: 26A33, 93B51, 93C95In this paper, design of fractional order digital differentiators and integrators using indirect discretization is presented. The proposed approach is based on using continued fraction expansion to find the rational approximation of the fractional order operator, s^α. The rational approximation thus obtained is discretized by using s to z transforms. The proposed approach is tested for differentiators and integrators of orders 1/4 and 1/2. The...