Common Fixed Point Theorems For Compatible Mapping Of Type (A) Involving Rational Contractive Condition

Sessa [11], initiated the tradition of improving commutativity conditions in metrical common fixed point theorems. While doing so Sessa [11] introduced the notion of weak commutativity. Motivated by Sessa [11], Jungck [6] generalized the concept of weak commuting by defining the term compatible mappings and proved that the weakly commuting mappings are compatible but the converse is not true. In recent years, several authors have obtained coincidence point results for various classes of mappings on a complete metric space utilizing these concepts. In this paper, we prove a common fixed point theorems for six mappings using the concept of compatible mapping of type (A). Our work generalizes some earlier results of Fisher [1], Jeong-Rhoades [4], Kannan [9] and others.