On approximate solutions of a functional equation in the class of differentiable functions
On approximate solutions of a system of functional equations
On approximate solutions of functional equations of countable order.
On approximate solutions of the Pexider equation.
On approximate solutions of the Pexider equation. (Summary).
On associative copulas uniformly close.
On associative developable surfaces
On axiomatic characterization of information-theoretic measure type
On Baire measurable solutions of some functional equations
We establish conditions under which Baire measurable solutions f of defined on a metrizable topological group are continuous at zero.
On Bimorphisms and Quadratic Forms on Groups
On Bimorphisms and Quadratic Forms on Groups. (Short Communications).
On boundaries of parallelizable regions of flows of free mappings.
On bounded time-dependent perturbations of operator cosine functions.
On boundedness and discontinuity of additive functions
On Cauchy differences of all orders.
On Cauchy-type functional equations.
On certain asymptotic functional equations.
On Characterizing x... .
On conjugacy equation in dimension one
In this paper, recent results on the existence and uniqueness of (continuous and homeomorphic) solutions φ of the equation φ ∘ f = g ∘ φ (f and g are given self-maps of an interval or the circle) are surveyed. Some applications of these results as well as the outcomes concerning systems of such equations are also presented.
On continuous composition operators
Let I ⊂ ℝ be an interval, Y be a normed linear space and Z be a Banach space. We investigate the Banach space Lip₂(I,Z) of all functions ψ: I → Z such that , where [r,s,t;ψ]:= ((s-r)ψ(t)+(t-s)ψ(r)-(t-r)ψ(s))/((t-r)(t-s)(s-r)). We show that ψ ∈ Lip₂(I,Z) if and only if ψ is differentiable and its derivative ψ’ is Lipschitzian. Suppose the composition operator N generated by h: I × Y → Z, (Nφ)(t):= h(t,φ(t)), maps the set (I,Y) of all affine functions φ: I → Y into Lip₂(I,Z). We prove that if N is...