Analytic Solutions of second order Nonlinear Difference Equations all of whose Eigenvalues are 1
Analytical formulas for solutions of linear difference equations.
Annular bounds for polynomial zeros and Schur stability of difference equations.
Applications of certain R-families
Applications of decomposable measures on nonlinear difference equations.
Applications of Extensions of Additive Functions.
Applications of Langenhop inequality to difference equations: Lower bounds and oscillation.
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 homomorphisms.
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 limit cycle of differential systems with variable coefficients
The behavior of the approximate solutions of two-dimensional nonlinear differential systems with variable coefficients is considered. Using a property of the approximate solution, so called conditional Ulam stability of a generalized logistic equation, the behavior of the approximate solution of the system is investigated. The obtained result explicitly presents the error between the limit cycle and its approximation. Some examples are presented with numerical simulations.