Dislocated metric space differs from metric space for a property that self distance of a point needs not to be equal to zero. This property plays an important role to deal with the problems of various disciplines to obtain fixed point results. In this article, we establish a common fixed point theorem for two pairs of weakly compatible mappings which generalize and extend the result of Brain Fisher [1] in the setting of dislocated metric space with replacement of contractive constant by contractive modulus for which continuity of mappings is not necessary and compatible mappings by weakly compatible mappings.

In this paper, the historical account of distances in metric space have introduced with generalize metric space which have applications to obtaining the solutions of various new important problems in nonlinear analysis.

In this paper, the historical account of fixed point results for single mapping in metric space has been provided. Though, there is a vast account of fixed point results for two or more mappings in the literature. It is mainly concentrated on single mapping due to our philosophical touch on Sthira Vindu (fixed point) and Kutastha Vindu in Vedanta philosophy.