On expanding iteration semigroups of set-valued functions.
On factorizing meromorphic functions.
On fractional iterates of a homeomorphism of the plane
We find all continuous iterative roots of nth order of a Sperner homeomorphism of the plane onto itself.
On functional equation ,
On functional inequalities in a single variable [Book]
On growth and zeros of differences of some meromorphic functions
On homeomorphic and diffeomorphic solutions of the Abel equation on the plane
We consider the Abel equation φ[f(x)] = φ(x) + a on the plane ℝ², where f is a free mapping (i.e. f is an orientation preserving homeomorphism of the plane onto itself with no fixed points). We find all its homeomorphic and diffeomorphic solutions φ having positive Jacobian. Moreover, we give some conditions which are equivalent to f being conjugate to a translation.
On iteration groups and related functional equations.
On iteration groups of certain functions
On iterative roots of a homeomorphism of the circle with an irrational rotation number.
On linear homogeneous functional equations in the indeterminate case
On locally bounded solutions of Schilling's problem
We prove that for some parameters q ∈ (0,1) every solution f:ℝ → ℝ of the functional equation f(qx) = 1/(4q) [f(x-1) + f(x+1) + 2f(x)] which vanishes outside the interval [-q/(1-q),q/(1-q)] and is bounded in a neighbourhood of a point of that interval vanishes everywhere.
On Nathanson's functional equation.
On nonstrict means.
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 quasi-continuous iteration groups on the unit circle.
On series-like iterative equation with a general boundary restriction.
On simultaneous Abel equations.
On solutions of a certain functional-integral equation