On the iteration of the hat-functions.
On the iterative process
On the k-pseudo-symmetrical approximate differentiability
On the Kurzweil integral for functions with values in ordered spaces. II.
On the limits of sequences of Darboux a.e. quasi-continuous functions
On the lower hull of convex functions.
On the maximum and the minimum of quasi-continuous functions
On the maximum of generalized Darboux functions
On the Moser-Onofri and Prékopa-Leindler inequalities.
Using elementary convexity arguments involving the Legendre transformation and the Prékopa-Leindler inequality, we prove the sharp Moser-Onofri inequality, which says that1/16π ∫|∇φ|2 + 1/4π ∫ φ - log (1/4π ∫ eφ) ≥ 0for any funcion φ ∈ C∞(S2).
On the nonlocal Cauchy problem for semilinear fractional order evolution equations
In this paper, we develop the approach and techniques of [Boucherif A., Precup R., Semilinear evolution equations with nonlocal initial conditions, Dynam. Systems Appl., 2007, 16(3), 507–516], [Zhou Y., Jiao F., Nonlocal Cauchy problem for fractional evolution equations, Nonlinar Anal. Real World Appl., 2010, 11(5), 4465–4475] to deal with nonlocal Cauchy problem for semilinear fractional order evolution equations. We present two new sufficient conditions on existence of mild solutions. The first...
On the number of minimal pairs of compact convex sets that are not translates of one another
Let [A,B] be the family of pairs of compact convex sets equivalent to (A,B). We prove that the cardinality of the set of minimal pairs in [A,B] that are not translates of one another is either 1 or greater than ℵ₀.
On the Operational Solution of a System of Fractional Differential Equations
MSC 2010: 26A33, 44A45, 44A40, 65J10We consider a linear system of differential equations with fractional derivatives, and its corresponding system in the field of Mikusiński operators, written in a matrix form, by using the connection between the fractional and the Mikusiński calculus. The exact and the approximate operational solution of the corresponding matrix equations, with operator entries are determined, and their characters are analyzed. By using the packages Scientific Work place and...
On the orbits of hat-functions
On the order of linear dependence of real functions
On the order of magnitude of Walsh-Fourier transform
For a Lebesgue integrable complex-valued function defined on let be its Walsh-Fourier transform. The Riemann-Lebesgue lemma says that as . But in general, there is no definite rate at which the Walsh-Fourier transform tends to zero. In fact, the Walsh-Fourier transform of an integrable function can tend to zero as slowly as we wish. Therefore, it is interesting to know for functions of which subclasses of there is a definite rate at which the Walsh-Fourier transform tends to zero. We...
On the points of quasicontinuity and cliquishness of functions
On the pointwise limits of sequences of Świątkowski functions
The characterization of the pointwise limits of the sequences of Świątkowski functions is given. Modifications of Świątkowski property with respect to different topologies finer than the Euclidean topology are discussed.
On the product of derivatives
On the product of derivatives
On the prolongation of restrictions of Baire 1 functions to functions which are quasicontinuous and approximately continuous
Let I ⊂ ℝ be an open interval and let A ⊂ I be any set. Every Baire 1 function f: I → ℝ coincides on A with a function g: I → ℝ which is simultaneously approximately continuous and quasicontinuous if and only if the set A is nowhere dense and of Lebesgue measure zero.