On continuity and monotonicity of Darboux transformations.
On continuous convex or concave functions with respect to the logarithmic mean
On continuous functions and the approximate symmetric derivatives
On continuous functions with no unilateral derivatives
We construct a family of continuous functions on the unit interval which have nowhere a unilateral derivative finite or infinite by using De Rham’s functional equations. Then we show that for any
On continuous interval functions
On Continuous Solutions of a Functional Inequality.
On contraction principle applied to nonlinear fractional differential equations with derivatives of order α ∈ (0,1)
One-term and multi-term fractional differential equations with a basic derivative of order α ∈ (0,1) are solved. The existence and uniqueness of the solution is proved by using the fixed point theorem and the equivalent norms designed for a given value of parameters and function space. The explicit form of the solution obeying the set of initial conditions is given.
On convergence for the -integral
On converse theorems of trigonometric approximation in weighted variable exponent Lebesgue spaces.
On convex functions bounded below.
On convex functions bounded below. (Short Communication).
On convex stochastic processes.
On convolution of continuous functions
On Darboux selections
On Darboux solutions of the Euler's equation.
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