About some properties of intermediate point in certain mean-value formulas.
About the existence and uniqueness of solution to fractional Bürger's equation.
About the Maximum and the Minimum of Darboux Functions
Absolute continuity and hyponormal operators.
Absolute continuity with respect to a subset of an interval
The aim of this paper is to introduce a generalization of the classical absolute continuity to a relative case, with respect to a subset of an interval . This generalization is based on adding more requirements to disjoint systems from the classical definition of absolute continuity – these systems should be not too far from and should be small relative to some covers of . We discuss basic properties of relative absolutely continuous functions and compare this class with other classes of...
Absolutely continuous invariant measures for C2 unimodal maps satisfying the Collet-Eckmann conditions.
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 >...
Abstract Perron-Stieltjes integral
Fundamental results concerning Stieltjes integrals for functions with values in Banach spaces are presented. The background of the theory is the Kurzweil approach to integration, based on Riemann type integral sums (see e.g. [4]). It is known that the Kurzweil theory leads to the (non-absolutely convergent) Perron-Stieltjes integral in the finite dimensional case. In [3] Ch. S. Honig presented a Stieltjes integral for Banach space valued functions. For Honig’s integral the Dushnik interior integral...
Abstract Riemann integrability and measurability
We prove that the spectral sets of any positive abstract Riemann integrable function are measurable but (at most) a countable amount of them. In addition, the integral of such a function can be computed as an improper classical Riemann integral of the measures of its spectral sets under some weak continuity conditions which in fact characterize the integral representation.
Addendum to the paper "Generalizations to monotonicity for uniform convergence of double sine integrals over ℝ̅ ²₊" (Studia Math. 201 (2010), 287-304)
Additive and convex functions in linear topological space.
Adjoint classes of functions in the sense
Using the concept of the -integral, we consider a similarly defined Stieltjes integral. We prove a Riemann-Lebesgue type theorem for this integral and give examples of adjoint classes of functions.
Affine Baire functions on Choquet simplices
We construct a metrizable simplex X such that for each n ɛ ℕ there exists a bounded function f on ext X of Baire class n that cannot be extended to a strongly affine function of Baire class n. We show that such an example cannot be constructed via the space of harmonic functions.
Algebraic properties of functions with the Cantor intermediate value property
Algebras of Borel measurable functions
We determine the size levels for any function on the hyperspace of an arc as follows. Assume Z is a continuum and consider the following three conditions: 1) Z is a planar AR; 2) cut points of Z have component number two; 3) any true cyclic element of Z contains at most two cut points of Z. Then any size level for an arc satisfies 1)-3) and conversely, if Z satisfies 1)-3), then Z is a diameter level for some arc.
Algunas consecuencias elementales del teorema de Weierstrass.
Almost continuous Darboux functions and Reed's pointwise convergence criteria
Almost Everywhere First-Return Recovery
We present a new characterization of Lebesgue measurable functions; namely, a function f:[0,1]→ ℝ is measurable if and only if it is first-return recoverable almost everywhere. This result is established by demonstrating a connection between almost everywhere first-return recovery and a first-return process for yielding the integral of a measurable function.
Almost iterable functions.
Almost midconvex and almost convex set-valued functions