Fixed Point Theory and Applications
Volume 2004 (2004), Issue 3, Pages 243-250

The aftermath of the intermediate value theorem

Raul Fierro,1 Carlos Martinez,1 and Claudio H. Morales2

1Departmento de Matemáticas, Pontificia Universidad Católica de Valparaiso, Casilla, Valparaiso 4059, Chile
2Department of Mathematics, University of Alabama in Huntsville, Huntsville 35899, AL, USA

Received 28 October 2003; Revised 27 January 2004

Copyright © 2004 Raul Fierro et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The solvability of nonlinear equations has awakened great interest among mathematicians for a number of centuries, perhaps as early as the Babylonian culture (3000–300 B.C.E.). However, we intend to bring to our attention that some of the problems studied nowadays appear to be amazingly related to the time of Bolzano's era (1781–1848). Indeed, this Czech mathematician or perhaps philosopher has rigorously proven what is known today as the intermediate value theorem, a result that is intimately related to various classical theorems that will be discussed throughout this work.