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

Abstract

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

Keywords

• fixed point in ℳvb–metric space and applications
• 47h10
• 54h25
• 55m20
• 37e10