Abstract—It is well-known that the classical Banach’s fixed point theorem has been generalized in various directions. This celebrated result has been extended to the theory of common fixed points. A few theorems dealing with the existence and uniqueness of common fixed points are presented here. These results not only extend but also sharpens some of the well known results found in the literature. There is a result which says that there does exist an improvement in the rate of convergence also.

Index Terms—Banach fixed point theorem, common fixed point, hilbert space, uniqueness.

The authors are with the Sardar Patel University, Vallabh Vidhya Nagar, Gujarat, India (e-mail: krishnappatel10@yahoo.com, gm.deheri@rediffmail.com).

Cite: Krishna P. Patel and G. M. Deheri, "Extension of Some Common Fixed Point Theorems," International Journal of Applied Physics and Mathematics vol. 3, no. 5, pp. 329-335, 2013.