Fixed point in 


ℳvb
M_{\rm{v}}^{\rm{b}}

– metric space and applications

Meena Joshi; Anita Tomar; Izhar Uddin

doi:10.2478/ausm-2023-0015

Abstract

The aim is to utilize a new metric called an $M_{v}^{b}$ 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 $M_{v}^{b}$ M_{\rm{v}}^{\rm{b}} –metric space. We demonstrate that the collection of open balls forms a basis on $M_{v}^{b}$ 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.

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

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