Fixed Point Theory and Applications 
Volume 2005 (2005), Issue 3, Pages 321-342
doi:10.1155/FPTA.2005.321

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

Abstract

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.