Summary: " Computing [Suppl] 15, 21-28 (2001)
@ Springer- Verlag 2001
Printed in Austria
On the Existence Theorems of Kantorovich, Moore and Miranda
G. E. Alefeld,Karlsruhe,F. A. Potra, Baltimore,and Z. Shen,Nanjing
Dedicated to Professor Tetsuro Yamamoto on the occasion of his 65th birthday
We show that the assumptions of the well-known Kantorovich theorem imply the assumptions of
Miranda's theorem, but not vice versa.
AMS Subject Classifications: 65HlO.
Key Words: Nonlinear systems, existence theorems, interval analysis.
The purpose of this paper is to show that the assumptions of the well-known
Kantorovich theorem imply the assumptions of Miranda's theorem. This sur-
prising fact can be conc1udedfrom aseries of well-known results on the existence
of solutions of a nonlinear system of equations in Rn. At the end of the paper we
give a short direct proof of this fact.
2. Some Existence Theorems and their Relations
Proving the existence of a solution of a system of nonlinear equations is a fun-