Fixed Point Theory and Applications
Volume 2004 (2004), Issue 3, Pages 243-250
doi:10.1155/S1687182004310053
The aftermath of the intermediate value theorem
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.
Abstract
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.