On the obstacle problem with a volume constraint.
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 Opial-Olech-Beesack inequalities.
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 Ostrowski type integral inequality.
On the points of non-differentiability of convex functions
We characterize sets of non-differentiability points of convex functions on . This completes (in ) the result by Zajíček [2] which gives a characterization of the magnitude of these sets.
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 power-series expansion of a rational function
Introduction. The problem of determining the formula for , the number of partitions of an integer into elements of a finite set S, that is, the number of solutions in non-negative integers, , of the equation hs₁ s₁ + ... + hsk sk = n, was solved in the nineteenth century (see Sylvester [4] and Glaisher [3] for detailed accounts). The solution is the coefficient of[(1-xs₁)... (1-xsk)]-1, expressions for which they derived. Wright [5] indicated a simpler method by which to find part of the solution...
On the precise asymptotics of the constant in Friedrich's inequality for functions vanishing on the part of the boundary with microinhomogeneous structure.
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.
On the proof of Erdős' inequality
Using undergraduate calculus, we give a direct elementary proof of a sharp Markov-type inequality for a constrained polynomial of degree at most , initially claimed by P. Erdős, which is different from the one in the paper of T. Erdélyi (2015). Whereafter, we give the situations on which the equality holds. On the basis of this inequality, we study the monotone polynomial which has only real zeros all but one outside of the interval and establish a new asymptotically sharp inequality.
On the properties of infinity-harmonic functions and an application to capacitary convex rings.
On the -analogue of gamma functions and related inequalities.
On the quasiarithmetic mean in a mean value property and the associated functional equation.
On the range of the derivative of a real-valued function with bounded support
We study the set f’(X) = f’(x): x ∈ X when f:X → ℝ is a differentiable bump. We first prove that for any C²-smooth bump f: ℝ² → ℝ the range of the derivative of f must be the closure of its interior. Next we show that if X is an infinite-dimensional separable Banach space with a -smooth bump b:X → ℝ such that is finite, then any connected open subset of X* containing 0 is the range of the derivative of a -smooth bump. We also study the finite-dimensional case which is quite different. Finally,...