About solutions of a functional equation.
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
About the use of a result of Professor Alexandru Lupaş to obtain some properties in the theory of the number .
Abschätzung der Teilsummen reeller Polynome.
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 functions of several variables and diffeomorphisms
In [4], a class of absolutely continuous functions of d-variables, motivated by applications to change of variables in an integral, has been introduced. The main result of this paper states that absolutely continuous functions in the sense of [4] are not stable under diffeomorphisms. We also show an example of a function which is absolutely continuous with respect cubes but not with respect to balls.
Absolutely continuous functions of two variables in the sense of Carathéodory.
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 convexity and Hermite-Hadamard type inequalities.
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.
Abstract separation theorems of Rodé type and their applications
Sufficient and necessary conditions are presented under which two given functions can be separated by a function Π-affine in Rodé sense (resp. Π-convex, Π-concave). As special cases several old and new separation theorems are obtained.
Abstract superposition operators on mappings of bounded variation of two real variables. II.
Abstract superposition operators on mappings of bounded variation of two real variables. I.
Accentuate the negative
A survey of mean inequalities with real weights is given.
Adams inequality on metric measure spaces.