Fixed Point Theory and Applications
Volume 2005 (2005), Issue 3, Pages 321-342

Existence of extremal solutions for quadratic fuzzy equations

Juan J. Nieto and Rosana Rodríguez-López

Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, Santiago de Compostela 15782, Spain

Received 8 November 2004; Revised 8 March 2005

Copyright © 2005 Juan J. Nieto and Rosana Rodríguez-López. 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.


Some results on the existence of solution for certain fuzzy equations are revised and extended. In this paper, we establish the existence of a solution for the fuzzy equation Ex2+Fx+G=x, where E, F, G, and x are positive fuzzy numbers satisfying certain conditions. To this purpose, we use fixed point theory, applying results such as the well-known fixed point theorem of Tarski, presenting some results regarding the existence of extremal solutions to the above equation.