Abstract. We give necessary and sufficient conditions for a pair of mappings to possess a common fixed point, which extend properly the results of Chang [3], Fisher [4], Jungck [5], Khan and Fisher [8], Rhoades, Tiwary and Singh [10] and Sessa, Mukherjee and Som [11]. As applications, the existence and uniqueness of common solutions for a class of functional equations in dynamic programming are discussed.

AMS Subject Classification (1991): 54H25, 47H10

Received October 16, 1997 and in revised form July 22, 1998. (Registered under 2691/2009.)