On the density of continuous functions in variable exponent Sobolev space.
On the derivative of indefinite RC-integral
On the derivative of type α
On the difference property of Borel measurable functions
If an atomlessly measurable cardinal exists, then the class of Lebesgue measurable functions, the class of Borel functions, and the Baire classes of all orders have the difference property. This gives a consistent positive answer to Laczkovich's Problem 2 [Acta Math. Acad. Sci. Hungar. 35 (1980)]. We also give a complete positive answer to Laczkovich's Problem 3 concerning Borel functions with Baire-α differences.
On the differences of upper semicontinuous quasi-continuous functions
On the differentiability of certain saltus functions
We investigate several natural questions on the differentiability of certain strictly increasing singular functions. Furthermore, motivated by the observation that for each famous singular function f investigated in the past, f’(ξ) = 0 if f’(ξ) exists and is finite, we show how, for example, an increasing real function g can be constructed so that for all rational numbers x and g’(x) = 0 for almost all irrational numbers x.
On the Differentiability of the Coordinate Functions of Póyla's Space-Filling Curve.
On the differentiation of convex functions
On the differentiation of convex functions in finite and infinite dimensional spaces
On the Dirichlet problem for functions of the first Baire class
Let be a simplicial function space on a metric compact space . Then the Choquet boundary of is an -set if and only if given any bounded Baire-one function on there is an -affine bounded Baire-one function on such that on . This theorem yields an answer to a problem of F. Jellett from [8] in the case of a metrizable set .
On the double Lusin condition and convergence theorem for Kurzweil-Henstock type integrals
Equiintegrability in a compact interval may be defined as a uniform integrability property that involves both the integrand and the corresponding primitive . The pointwise convergence of the integrands to some and the equiintegrability of the functions together imply that is also integrable with primitive and that the primitives converge uniformly to . In this paper, another uniform integrability property called uniform double Lusin condition introduced in the papers E. Cabral...
On the Durrmeyer-type modification of some discrete approximation operators.
On the embedding
On the embedding Waterman, Chanturia and generalized Wiener classes in the classes .
On the entropy of Darboux functions
We prove some results concerning the entropy of Darboux (and almost continuous) functions. We first generalize some theorems valid for continuous functions, and then we study properties which are specific to Darboux functions. Finally, we give theorems on approximating almost continuous functions by functions with infinite entropy.
On the equality condition in Hölder's and Minkowski inequalities.
On the equality condition in Hölder's and Minkowski's inequalities. (Summary).
On the equation
On the Equivalence of the Riemann-Liouville and the Caputo Fractional Order Derivatives in Modeling of Linear Viscoelastic Materials
Mathematics Subject Classification: 26A33In the process of constructing empirical mathematical models of physical phenomena using the fractional calculus, investigators are usually faced with the choice of which definition of the fractional derivative to use, the Riemann-Liouville definition or the Caputo definition. This investigation presents the case that, with some minimal restrictions, the two definitions produce completely equivalent mathematical models of the linear viscoelastic phenomenon....
On the estension of Lipschitz functions with respect to two Hilbert norms and two Lipschitz conditions