Function decompositions related to the Luzin N-property.
Functional equations and nowhere differentiable functions.
Functional equations and nowhere differentiable functions. (Summary).
Functional equations for pecular functions.
Functional inequality characterizing nonnegative concave functions in (0, ?)k.
Functional inequality characterizing nonnegative concave functions in (0, ?)k. (Summary).
Functions characterized by images of sets
For non-empty topological spaces X and Y and arbitrary families ⊆ and we put =f ∈ : (∀ A ∈ )(f[A] ∈ . We examine which classes of functions ⊆ can be represented as . We are mainly interested in the case when is the class of all continuous functions from X into Y. We prove that for a non-discrete Tikhonov space X the class (X,ℝ) is not equal to for any ⊆ and ⊆ (ℝ). Thus, (X,ℝ) cannot be characterized by images of sets. We also show that none of the following classes of...
Functions having the Darboux property and satisfying some functional equation
Let X be a real linear topological space. We characterize solutions f:X → ℝ and M:ℝ → ℝ of the equation f(x+M(f(x))y) = f(x)f(y) under the assumption that f and M have the Darboux property.
Functions of Baire class one
Let K be a compact metric space. A real-valued function on K is said to be of Baire class one (Baire-1) if it is the pointwise limit of a sequence of continuous functions. We study two well known ordinal indices of Baire-1 functions, the oscillation index β and the convergence index γ. It is shown that these two indices are fully compatible in the following sense: a Baire-1 function f satisfies for some countable ordinals ξ₁ and ξ₂ if and only if there exists a sequence (fₙ) of Baire-1 functions...
Functions of finite fractional variation and their applications to fractional impulsive equations
We introduce a notion of a function of finite fractional variation and characterize such functions together with their weak -additive fractional derivatives. Next, we use these functions to study differential equations of fractional order, containing a -additive term—we prove existence and uniqueness of a solution as well as derive a Cauchy formula for the solution. We apply these results to impulsive equations, i.e. equations containing the Dirac measures.
Functions of generalized variation
Functions of slow increase and integer sequences.
Functions Riemann-Stieltjes integrable against themselves
Functions satisfying an integral Lipschitz condition
Fundamental solutions to the fractional heat conduction equation in a ball under Robin boundary condition
The central symmetric time-fractional heat conduction equation with Caputo derivative of order 0 < α ≤ 2 is considered in a ball under two types of Robin boundary condition: the mathematical one with the prescribed linear combination of values of temperature and values of its normal derivative at the boundary, and the physical condition with the prescribed linear combination of values of temperature and values of the heat flux at the boundary, which is a consequence of Newton’s law of convective...
Fundamental theorems of analysis in formally real fields.
Funktionen von beschränkter Variation auf metrischen Räumen.
Further reverse results for Jensen's discrete inequality and applications in information theory.
Gauge integrals and series
This note contains a simple example which does clearly indicate the differences in the Henstock-Kurzweil, McShane and strong McShane integrals for Banach space valued functions.
General exact solvability conditions for the initial value problems for linear fractional functional differential equations
Conditions on the unique solvability of linear fractional functional differential equations are established. A pantograph-type model from electrodynamics is studied.