An Odd Solution to the Functional Equation ... = exp (P(x)).
Analogs of Bernoulli polynomials in fields Zp.
Analytic roots of invertible matrix functions.
Analytic solutions for polynomial-like iterative equations with variable coefficients
Analytic solutions of polynomial-like iterative functional equations with variable coefficients are discussed in the complex field ℂ by reducing to an auxiliary equation and by applying known results for systems of nonlinear functional equations of finite orders.
Analytic solutions of a nonlinear two variables difference system whose eigenvalues are both 1
For nonlinear difference equations, it is difficult to obtain analytic solutions, especially when all the eigenvalues of the equation are of absolute value 1. We consider a second order nonlinear difference equation which can be transformed into the following simultaneous system of nonlinear difference equations: ⎧ x(t+1) = X(x(t),y(t)) ⎨ ⎩ y(t+1) = Y(x(t), y(t)) where , satisfy some conditions. For these equations, we have obtained analytic solutions in the cases "|λ₁| ≠ 1 or |λ₂| ≠ 1" or "μ...
Analytic solutions of Böttcher's functional equation in the unit disk.
Applications of certain R-families
Applications of Extensions of Additive Functions.
Applications of the -adic Nevanlinna theory to functional equations
Let be an algebraically closed field of characteristic zero, complete for an ultrametric absolute value. We apply the -adic Nevanlinna theory to functional equations of the form , where , are meromorphic functions in , or in an “open disk”, satisfying conditions on the order of its zeros and poles. In various cases we show that and must be constant when they are meromorphic in all , or they must be quotients of bounded functions when they are meromorphic in an “open disk”. In particular,...
Applications of the zero-one law to problems connected with Cauchy's functional equation.
Approximate behavior of bi-quadratic mappings in quasinormed spaces.
Approximate solutions of the generalized Goła̧b-Schinzel equation.
Approximate tri-quadratic functional equations via Lipschitz conditions
In this paper, we consider Lipschitz conditions for tri-quadratic functional equations. We introduce a new notion similar to that of the left invariant mean and prove that a family of functions with this property can be approximated by tri-quadratic functions via a Lipschitz norm.
Approximately -Jordan homomorphisms on Banach algebras.
Approximately partial ternary quadratic derivations on Banach ternary algebras.
Approximately quadratic mappings on restricted domains.
Approximation of a mixed functional equation in quasi-Banach spaces.
Approximation of generalized homomorphisms in quasi-Banach algebras.
Approximation of generalized left derivations.
Approximation of mixed type functional equations in -Banach spaces.