We first introduce a new concept of b-dislocated metric space as a generalization of
dislocated metric space and analyze different properties of such spaces.
A fundamental result for the convergence of sequences in b-dislocated metric spaces
is established and is employed to prove some common fixed point results for four
mappings satisfying the generalized weak contractive condition in partially ordered
b-dislocated metric spaces. Moreover, some examples and applications to integral
equations are given here to illustrate the usability of the obtained results.