Proving Common Fixed Point Theorems for Lipschitz Type Mappings via Absorbing Pair

Our aim in the present paper is three fold. Firstly, we obtain a common fixed point theorem for a pair of self mappings satisfying a Lipschitz type condition employing the property (E.A.) along with a relatively new notion of absorbing pair of maps wherein we never require conditions on the completeness of the space, containment of range of one mapping into the range of other, continuity of the mappings involved besides a set of unusual alternative conditions as utilized by Pant. Secondly, we further improve our first result by replacing the Lipschitz (or non-contractive) type condition with g-continuity of the mapping f . Thirdly, in our last result, we observe that if we restrict ourselves to non-compatibility instead of the property (E.A.) in our first result, then the maps turn out to be discontinuous at their common fixed point. We also furnish illustrative examples to demonstrate the utility of our results over related ones.