Abstract
We discuss the existence of a fixed point for a self mapping and its uniqueness satisfying (ϕ˙, η˙) -generalized contractive condition including altering distance functions of rational terms in an ordered b-metric space. It is also discussed whether the two self-maps under the same contraction condition can be coincident and coupled coincident. The results are backed up by a dearth of numerical examples and application to nonlinear quadratic integral equation.