About the Maximum and the Minimum of Darboux Functions
Absolutely convergent Fourier series and generalized Lipschitz classes of functions
We investigate the order of magnitude of the modulus of continuity of a function f with absolutely convergent Fourier series. We give sufficient conditions in terms of the Fourier coefficients in order that f belong to one of the generalized Lipschitz classes Lip(α,L) and Lip(α,1/L), where 0 ≤ α ≤ 1 and L = L(x) is a positive, nondecreasing, slowly varying function such that L(x) → ∞ as x → ∞. For example, a 2π-periodic function f is said to belong to the class Lip(α,L) if for all x ∈ , h >...
Algebraic properties of functions with the Cantor intermediate value property
Alternative definitions of -density topology
An abstract version of Sierpiński's theorem and the algebra generated by A and CA functions
We give an abstract version of Sierpiński's theorem which says that the closure in the uniform convergence topology of the algebra spanned by the sums of lower and upper semicontinuous functions is the class of all Baire 1 functions. Later we show that a natural generalization of Sierpiński's result for the uniform closure of the space of all sums of A and CA functions is not true. Namely we show that the uniform closure of the space of all sums of A and CA functions is a proper subclass of the...
An example of a function which is locally constant in an open dense set, everywhere differentiable but not constant
An extension of Brunovský's Scorza-Dragoni type theorem for unbounded set-valued functions
Analyse 2-microlocale et développementen série de chirps d'une fonction de Riemann et de ses généralisations
En dimension 1 on analyse la fonction irrégulière (p entier ≥ 2) en un point de dérivabilité (π est un tel point) et on démontre que le terme d’erreur est un chirp de classe (1 + 1/(2p-2), 1/(p-1), (p-1)/p). La fonction r(x) est dans l’espace 2-microlocal si et seulement si s+s’ ≤ 1 - 1/p et ps+s’≤ p - 1/2. En dimension 2, on obtient en (π,π) l’existence d’un plan tangent pour la surface dès que γ>1.
Approximate maxima
Arrow-Hahn economic models with weakened conditions of continuity
In this article we give descriptions of some economic models that are based on Arrow-Hahn economic model. Finally we consider a model with two major assumptions: first, there is discontinuous excess demand function and, second, if price goes to zero, then it is possible that excess demand may approach infinity. For this last new economic model the existence of quasi-equilibrium is proved.
Asymptotic Formulae for Recursively Defined Baskakov-type Operators
Averages of quasi-continuous functions
The goal of this paper is to characterize the family of averages of comparable (Darboux) quasi-continuous functions.
Baire classification of ...-density and ...-approximately continous functions.
Baire functions and their restrictions to special sets
Characteristic Types of Convergence for Certain Classes of Darboux-Baire 1 Functions
Characterizations of Connected Real Functions.
Characterizations of real functions by continua
Characterizations of -stratifiable spaces
Classes of Weighted Symmetric Functions
Composition of functions.