On points of qualitative semicontinuity
On pointwise interpolation inequalities for derivatives
Pointwise interpolation inequalities, in particular, ku(x)c(Mu(x)) 1-k/m (Mmu(x))k/m, k<m, and |Izf(x)|c (MIf(x))Re z/Re (Mf(x))1-Re z/Re , 0<Re z<Re<n, where is the gradient of order , is the Hardy-Littlewood maximal operator, and is the Riesz potential of order , are proved. Applications to the theory of multipliers in pairs of Sobolev spaces are given. In particular, the maximal algebra in the multiplier space is described.
On pointwise limits of sequences of -continuous functions
On polynomials of Sheffer type arising from a Cauchy problem.
On preponderant maxima
On principal iteration semigroups in the case of multiplier zero
We collect and generalize various known definitions of principal iteration semigroups in the case of multiplier zero and establish connections among them. The common characteristic property of each definition is conjugating of an iteration semigroup to different normal forms. The conjugating functions are expressed by suitable formulas and satisfy either Böttcher’s or Schröder’s functional equation.
On Probability Distribution Solutions of a Functional Equation
Let 0 < β < α < 1 and let p ∈ (0,1). We consider the functional equation φ(x) = pφ (x-β)/(1-β) + (1-p)φ(minx/α, (x(α-β)+β(1-α))/α(1-β)) and its solutions in two classes of functions, namely ℐ = φ: ℝ → ℝ|φ is increasing, , , = φ: ℝ → ℝ|φ is continuous, , . We prove that the above equation has at most one solution in and that for some parameters α,β and p such a solution exists, and for some it does not. We also determine all solutions of the equation in ℐ and we show the exact connection...
On q–Analogues of Caputo Derivative and Mittag–Leffler Function
Mathematics Subject Classification: 33D60, 33E12, 26A33Based on the fractional q–integral with the parametric lower limit of integration, we consider the fractional q–derivative of Caputo type. Especially, its applications to q-exponential functions allow us to introduce q–analogues of the Mittag–Leffler function. Vice versa, those functions can be used for defining generalized operators in fractional q–calculus.
On quadrature rules, inequalities and error bounds.
On qualitative cluster sets
On quasicontinuous and cliquish functions
On quasi-continuous bijections.
On quasi-continuous functions having Darboux property.
On quasi-continuous iteration semigroups and groups of real functions
On quasi-uniform convergence of a sequence of s.q.c. functions
On realizability of sign patterns by real polynomials
The classical Descartes’ rule of signs limits the number of positive roots of a real polynomial in one variable by the number of sign changes in the sequence of its coefficients. One can ask the question which pairs of nonnegative integers , chosen in accordance with this rule and with some other natural conditions, can be the pairs of numbers of positive and negative roots of a real polynomial with prescribed signs of the coefficients. The paper solves this problem for degree polynomials.
On refinements of Aczél, Popoviciu, Bellman's inequalities and related results.
On refinements of certain inequalities for means
In this paper we obtain certain refinements (and new proofs) for inequalities involving means, results attributed to Carlson; Leach and Sholander; Alzer; Sndor; and Vamanamurthy and Vuorinen.
On Regularly Varying Functions With Applications To Functions Theory.
On relations among metric derived numbers