Hilbert space

The solution of an infinite system of ternary differential equations

The present paper is devoted to an infinite system of differential equations.  This system consists of ternary differential equations  corresponding to $3\times3$ Jordan blocks.  The system is considered in the Hilbert space $l_2$.  A theorem about the existence and uniqueness of solution of the system is proved.

Enlarging the radius of convergence for Newton–like method in which the derivative is re-evaluated after certain steps

Numerous attempts have been made to enlarge the radius of convergence for Newton–like method under the same set of conditions.  It turns out that not only the radius of convergence but the error bounds on the distances involved and the uniqueness of the solution ball  can more accurately be defined.