On the midpoint quadrature formula for lipschitzian mappings and applications
On the midpoint quadrature formula for mappings with bounded variations and applications
On the Minkowski-Hölder type inequalities for generalized Sugeno integrals with an application
In this paper, we use a new method to obtain the necessary and sufficient condition guaranteeing the validity of the Minkowski-Hölder type inequality for the generalized upper Sugeno integral in the case of functions belonging to a wider class than the comonotone functions. As a by-product, we show that the Minkowski type inequality for seminormed fuzzy integral presented by Daraby and Ghadimi [11] is not true. Next, we study the Minkowski-Hölder inequality for the lower Sugeno integral and the...
On the monotonicity and log-convexity of a four-parameter homogeneous mean.
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 notions of absolute continuity for functions of several variables
Absolutely continuous functions of n variables were recently introduced by J. Malý [5]. We introduce a more general definition, suggested by L. Zajíček. This new absolute continuity also implies continuity, weak differentiability with gradient in Lⁿ, differentiability almost everywhere and the area formula. It is shown that our definition does not depend on the shape of balls in the definition.
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 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.