Fixed point in ℳvb M_{\rm{v}}^{\rm{b}} – metric space and applications

The aim is to utilize a new metric called an Mvb M_{\rm{v}}^{\rm{b}} –metric which is an improvement and generalization of M_v−metric to revisit the celebrated Banach and Sehgal contractions in Mvb M_{\rm{v}}^{\rm{b}} –metric space. We demonstrate that the collection of open balls forms a basis on Mvb 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.