Abstract—This investigation aims to establish the importance of weak reciprocal continuity of the maps in deriving the common fixed point theorems. The existence and uniqueness of the common fixed points are obtained under generalized contractive conditions in the setting of complete metric spaces. That the rate of convergence is duly addressed is manifest in the proofs.

Index Terms—Complete metric space, fixed point, weak reciprocal continuity, compatibility.

The authors are with the Department of Mathematics from the Sardar Patel University at Vallabh Vidhyanagar-388120, Gujarat, India (e-mail: ekta301190@gmail.com, gm.deheri@rediffmail.com).

Cite: Ekta H. Patel and G. M. Deheri, "Weak Reciprocal Continuity and Common Fixed Point Theorems," International Journal of Applied Physics and Mathematics vol. 4, no. 3, pp. 159-165, 2014.