Fixed Point Theory and Applications
Volume 2004 (2004), Issue 3, Pages 243-250
doi:10.1155/S1687182004310053
The aftermath of the intermediate value theorem
Raul Fierro1
, Carlos Martinez1
and Claudio H. Morales3
1Departmento de Matemáticas, Pontificia Universidad Católica de Valparaiso, Casilla, Valparaiso 4059, Chile
3Department of Mathematics, University of Alabama in Huntsville, Huntsville 35899, AL, USA
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.