The aim of this research paper is to extend the results of Karapinar and Khojasteh [13], Karapinar and Fluga [12] in super metric space using the weakly compatible mappings. Further, the analogue results of Jungck [10], Das and Naik [6] and Ciric [5] in quasi- contraction mappings are generalized in super metric space.
Considering Banach pioneering fixed point theorem, a large number of results have been observed. Normally, there are two main features which are used to extend and generalize the metric fixed point theory. Either the contractive conditions are weakened or abstract structure is changed.
The well-known Banach contraction mapping principle states that if 𝑓: 𝑋 → 𝑋 is a contraction on 𝑋 ( i. e. d(fx, fy)≤qd(x, y) for some q <1andallx, y∈X) and X is complete , then f has a unique fixed point.
A large number of generalization of this result have appeared in the literature of fixed point theory. Ciric [5] introduced and studied quasi-contraction as one of the most general contractive type map.