A GENERALIZED THEOREM OF MIRANDA AND THE THEOREM OF NEWTON–KANTOROVICH
Jan Mayer · Numerical Functional Analysis and Optimization · 2002
In this paper, we discuss the theorems of Newton–Kantorovich, the Theorem of Miranda, and the relationship between them. We begin by generalizing Miranda's theorem and propose a converse. Then we show that mappings satisfying the assumptions of the Theorem of Newton–Kantorovich in a strong sense automatically satisfy those of our generalization of Miranda's theorem. This relationship yields in particular an explicit way of determining the signum of a function on the boundary of given sets.