Orbital continuity and fixed points

The aim of the present paper is to show the significance of the concept of orbital continuity introduced by Ciric. We prove that orbital continuity of a pair of R-weak commuting self-mappings of type A_f or of type A_g of a complete metric space is equivalent to fixed point property under Jungck type contraction. We also establish a situation in which orbital continuity is a necessary and sufficient condition for the existence of a common fixed point of a pair of mappings yet the mappings are necessarily discontinuous at the fixed point.