Abstract—The celebrated Banach fixed point theorem has been modified and developed in various aspects. It is not surprising all that this result admits several generalizations and improvement. Besides a good number of variations of the generalizations of the result are formed today. A few theorems dealing with existence and uniqueness of the fixed points are presented hear. This result not only extend the variation of the generalization of the Banach fixed point theorem but also improve the result. In addition the rate of convergence is found to be better.

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

The authors are with Saradar Patel University, Vallabh Vidhyanagar, Gujarat, India (email: binapatel7777856@gamil.com).

Cite: Bina R. Patel, G. M. Deheri, "Extension of Some Common Fixed Point Theorems," International Journal of Applied Physics and Mathematics vol. 6, no. 4, pp. 172-184, 2016.