On Fuzzy Volterra Integral Equations with Deviating Arguments

In 1982, Dubois and Prade [4, 5] first introduced the concept of integration of fuzzy functions. Kaleva [7] studied the measurability and integrability for the fuzzy set-valued mappings of a real variable whose values are normal, convex, upper semicontinuous, and compactly supported by fuzzy sets in Rn. Existence of solutions of fuzzy integral equations has been studied by several authors [1, 2, 7, 8]. Subrahmanyam and Sudarsanam [13] proved existence theorems for fuzzy functional equations. They have used the embedding theorem of Kaleva [8], which is a generalization of the classical Rådström embedding theorem [11], and the Darbo fixed point theorem in the convex cone. Recently, Balachandran and Prakash [2, 3] studied the existence of solutions of nonlinear fuzzy Volterra-Fredholm integral equations. In this paper, we prove the existence of solutions of fuzzy Volterra integral equations with deviating arguments. The results, which generalize the results of [1, 2], are established with the help of the Darbo fixed point theorem. Further, we study the maximal solution of the fuzzy delay Volterra integral equation.