Abstract—In this paper we studied a class of Volterra integral equation by using Mönch fixed point theorem, we intend to offer new numerical methods to solve the fuzzy Volterra- Fredholm integro-integral equations. By using the comparison theorems and Picard iterated approximation method we obtained the existence theorem of the solution under some weaker conditions, and we proved the theorem. Some examples are investigated to verify convergence results and to illustrate the efficiently of the method.

Index Terms—Fuzzy integral equations, fuzzy number space, measure of noncompactness, mönch fixed point theorem.

Fan Guanghui is with Department of Mathematics, Heilongjiang Institute of Technology, Harbin, China, 150050 (email: fghxyz@163.com).

Cite: Fan Guanghui, "A Note on Fuzzy Volterra-Fredholm Integro-Integral Equations," International Journal of Applied Physics and Mathematics vol. 7, no. 1, pp. 59-68, 2017.