On Cauchy differences of all orders.
On Cauchy-type functional equations.
On certain asymptotic functional equations.
On certain comparison theorems for half-linear dynamic equations on time scales.
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...
On continuous convex or concave functions with respect to the logarithmic mean
On continuous preservation of norms and areas.
On Continuous Solutions of a Functional Equation.
On continuous solutions of a functional equation
This paper discusses continuous solutions of the functional equation φ[f(x)] = g(x,φ(x)) in topological spaces.
On continuous solutions of systems of functional equations
On continuous solutions of the Schröder equation
On convex and *-concave multifunctions
A continuous multifunction F:[a,b] → clb(Y) is *-concave if and only if the inclusion holds for every s,t ∈ [a,b], s < t.
On convex stochastic processes.
On convex triangle functions.
On convolution type functional equations.
On Costas sets and Costas clouds.
On curves invariant under an axial transform
On D'Alembert's functional equation on a Abelian group.