Approximation by continuous functions in the Fell topology

We study the approximation of multivalued functions in the Fell topology by means of single valued continuous functions or minimal upper semicontinuous compact-valued maps. We give a partial answer to Question 5.5 in [R.A. McCoy, Comparison of hyperspace and function space topologies, in: G. Di Maio, L. Holá, (Eds.), Recent Progress in Function Spaces, in: Quad. Mat., vol. 3, Aracne Editrice, Caserta, 1998, pp. 241–251] and to Question 7 in [R.A. McCoy, Fell topology and uniform topology on compacta on spaces of multifunctions, Rostock. Math. Kolloq. 51 (1997) 127–136].