On nowhere density of the class of somewhat continuous functions in
On nowhere weakly symmetric functions and functions with two-element range
A function f: ℝ → {0,1} is weakly symmetric (resp. weakly symmetrically continuous) at x ∈ ℝ provided there is a sequence hₙ → 0 such that f(x+hₙ) = f(x-hₙ) = f(x) (resp. f(x+hₙ) = f(x-hₙ)) for every n. We characterize the sets S(f) of all points at which f fails to be weakly symmetrically continuous and show that f must be weakly symmetric at some x ∈ ℝ∖S(f). In particular, there is no f: ℝ → {0,1} which is nowhere weakly symmetric. It is also shown that if at each point x we...
On one class of operators associated with differential equations of fractional order.
On one-sided BMO and Lipschitz functions
On Pawlak's problem concerning entropy of almost continuous functions
We prove that if f: → is Darboux and has a point of prime period different from , i = 0,1,..., then the entropy of f is positive. On the other hand, for every set A ⊂ ℕ with 1 ∈ A there is an almost continuous (in the sense of Stallings) function f: → with positive entropy for which the set Per(f) of prime periods of all periodic points is equal to A.
On points of absolute continuity, III
On points of qualitative semicontinuity
On pointwise limits of sequences of -continuous functions
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 Regularly Varying Functions With Applications To Functions Theory.
On relations among metric derived numbers