On the differentiability of solutions of a functional equation with respect to a parameter
This contribution deals with the dominance relation on the class of conjunctors, containing as particular cases the subclasses of quasi-copulas, copulas and t-norms. The main results pertain to the summand-wise nature of the dominance relation, when applied to ordinal sum conjunctors, and to the relationship between the idempotent elements of two conjunctors involved in a dominance relationship. The results are illustrated on some well-known parametric families of t-norms and copulas.
Necessary and sufficient conditions for the existence of compactly supported -solutions for the two-dimensional two-scale dilation equations are given.
The neutral delay difference equations of second order with positive and negative coefficients , n = 0,1,2,... studied sufficient condition existence positive solution equation obtained
We consider a second order nonlinear difference equation The necessary conditions under which there exists a solution of equation (E) which can be written in the form Here and are two linearly independent solutions of equation A special case of equation (E) is also considered.