A backward three-term recurrence relation for vector valued continued fractions and its applications

This paper presents a backward three-term recurrence relation, which is a solution of an open problem in Graves-Morris (Numer. Math. 42 (1983) 331). By means of this relation, we succeed in establishing some conclusions about the two backward successive convergents of vector valued continued fractions. Moreover, an expression for the vector valued continued fraction in series form is obtained and some theorems of the convergence of the vector valued continued fraction are proved by virtue of the recurrence relation.