 
Summary: " Computing [Suppl] 15, 2128 (2001)
Computing
@ 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
Abstract
We show that the assumptions of the wellknown 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.
1. Introduction
The purpose of this paper is to show that the assumptions of the wellknown
Kantorovich theorem imply the assumptions of Miranda's theorem. This sur
prising fact can be conc1udedfrom aseries of wellknown 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
