The aim is to utilize a new metric called an
M_{\rm{v}}^{\rm{b}}
–metric which is an improvement and generalization of Mv−metric to revisit the celebrated Banach and Sehgal contractions in
M_{\rm{v}}^{\rm{b}}
–metric space. We demonstrate that the collection of open balls forms a basis on
M_{\rm{v}}^{\rm{b}}
-metric space. Further, we give some examples for the verification of established results. Towards the end, we solve a non-linear matrix equation and an equation of rotation of a hanging cable to substantiate the utility of these extensions.