CONTENTS Introduction.....................................................................................................................................................................................................5 1. Some properties of multi-valued functions...................................................................................................................................................5 2. Fixed-point theorems for multi-valued functions.........................................................................................................................................11 3. On the characterization and extension of continuous solutions of functional equation with multi-valued functions...................................17 4. On the existence of continuous solutions of functional equations of n-th order with multi-valued functions..............................................21 5. On the continuous solutions of a functional inequality...............................................................................................................................25 References.....................................................................................................................................................................................................28