On decomposing the plane into connected or one-to-one curves
On Denjoy property and on approximate partial derivatives
On Denjoy type extensions of the Pettis integral
In this paper two Denjoy type extensions of the Pettis integral are defined and studied. These integrals are shown to extend the Pettis integral in a natural way analogous to that in which the Denjoy integrals extend the Lebesgue integral for real-valued functions. The connection between some Denjoy type extensions of the Pettis integral is examined.
On Denjoy-Dunford and Denjoy-Pettis integrals
The two main results of this paper are the following: (a) If X is a Banach space and f : [a,b] → X is a function such that x*f is Denjoy integrable for all x* ∈ X*, then f is Denjoy-Dunford integrable, and (b) There exists a Dunford integrable function which is not Pettis integrable on any subinterval in [a,b], while belongs to for every subinterval J in [a,b]. These results provide answers to two open problems left by R. A. Gordon in [4]. Some other questions in connection with Denjoy-Dundord...
On derivations on certain function spaces and their relation to the differential operator. (Über Derivationen auf gewissen Funktionenräumen und deren Beziehung zum Differentiationsoperator.)
On derivatives of functions defined on disconnected sets, I
On derivatives of functions defined on disconnected sets, II
On derivo-periodic multifunctions
The problem of linearity of a multivalued derivative and consequently the problem of necessary and sufficient conditions for derivo-periodic multifunctions are investigated. The notion of a derivative of multivalued functions is understood in various ways. Advantages and disadvantages of these approaches are discussed.
On determining sets for the class of somewhat continuous functions
On differentiability of Peano type functions
On differentiability of Peano type functions
On differentiability of Peano type functions. II
On differentiability with respect to parameters of the Lebesgue integral.
On Dini Derivatives and on a Property of Denjoy.
On Dini derivatives and on certain classes of Zahorski
On embedding of the class .
On entropy of patterns given by interval maps
Defining the complexity of a green pattern exhibited by an interval map, we give the best bounds of the topological entropy of a pattern with a given complexity. Moreover, we show that the topological entropy attains its strict minimum on the set of patterns with fixed eccentricity m/n at a unimodal X-minimal case. Using a different method, the last result was independently proved in[11].
On equations and properties concerning some classes of chordal polygons.
On equivalence of coefficient conditions.
On equivalence of coefficient conditions. II.