Teoremi di regolarità per una classe di equazioni funzionali
Ternary Jordan homomorphisms in -ternary algebras.
The Abel equation and total solvability of linear functional equations
We investigate the solvability in continuous functions of the Abel equation φ(Fx) - φ(x) = 1 where F is a given continuous mapping of a topological space X. This property depends on the dynamics generated by F. The solvability of all linear equations P(x)ψ(Fx) + Q(x)ψ(x) = γ(x) follows from solvability of the Abel equation in case F is a homeomorphism. If F is noninvertible but X is locally compact then such a total solvability is determined by the same property of the cohomological equation φ(Fx)...
The addition formula for theta functions.
The addition theorem of Weierstrass' s sigma function.
The additive approximation on a four-variate Jensen-type operator equation.
The associativity equation revisited.
The Beckman-Quarles theorem for mappings from to .
The Binet-Pexider functional equation for rectangular matrices.
The solutions of the series-like iterative equation with variable coefficients.
The cardinality of the set of discontinuous solutions of a class of functional equations.
The Christensen measurable solutions of a generalization of the Gołąb-Schinzel functional equation
Let K denote the set of all reals or complex numbers. Let X be a topological linear separable F-space over K. The following generalization of the result of C. G. Popa [16] is proved. Theorem. Let n be a positive integer. If a Christensen measurable function f: X → K satisfies the functional equation , then it is continuous or the set x ∈ X : f(x) ≠ 0 is a Christensen zero set.
The cocycle equation in division rings.
The Complete Solution of Hosszú's Functional Equation Over a Field. (Short Communication).
The Complete Solution of Hosszú's Functional Equation Over a Field.
The continuous solution of a functional equation of Abel.
The continuous solutions of a generalized Dhombres functional equation
We consider the functional equation where is a given increasing homeomorphism of an open interval and is an unknown continuous function. In a series of papers by P. Kahlig and J. Smítal it was proved that the range of any non-constant solution is an interval whose end-points are fixed under and which contains in its interior no fixed point except for . They also provide a characterization of the class of monotone solutions and prove a necessary and sufficient condition for any solution...
The convergence of an implicit mean value iteration.
The converse problem for a generalized Dhombres functional equation
We consider the functional equation where is a given homeomorphism of an open interval and is an unknown continuous function. A characterization of the class of continuous solutions is given in a series of papers by Kahlig and Smítal 1998–2002, and in a recent paper by Reich et al. 2004, in the case when is increasing. In the present paper we solve the converse problem, for which continuous maps , where is an interval, there is an increasing homeomorphism of such that . We...
The cosine functional equation for nilpotent groups.