<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The aim is to utilize a new metric called an <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2023-0015_eq_002.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>M</mi></mrow><mtext>v</mtext><mtext>b</mtext></msubsup></mrow></math>
<tex-math>M_{\rm{v}}^{\rm{b}}</tex-math>
</alternatives>
</inline-formula>–metric which is an improvement and generalization of M<sub>v</sub>−metric to revisit the celebrated Banach and Sehgal contractions in <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2023-0015_eq_003.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>M</mi></mrow><mtext>v</mtext><mtext>b</mtext></msubsup></mrow></math>
<tex-math>M_{\rm{v}}^{\rm{b}}</tex-math>
</alternatives>
</inline-formula>–metric space. We demonstrate that the collection of open balls forms a basis on <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2023-0015_eq_004.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>M</mi></mrow><mtext>v</mtext><mtext>b</mtext></msubsup></mrow></math>
<tex-math>M_{\rm{v}}^{\rm{b}}</tex-math>
</alternatives></inline-formula>-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.</p>
</abstract>

The aim is to utilize a new metric called an 


Mvb
M_{\rm{v}}^{\rm{b}}

–metric which is an improvement and generalization of Mv−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.

Fixed point in <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2023-0015_eq_001.png"/>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>ℳ</mi></mrow><mtext>v</mtext><mtext>b</mtext></msubsup></mrow></math>
<tex-math>M_{\rm{v}}^{\rm{b}}</tex-math>
</alternatives>
</inline-formula>– metric space and applications

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Fixed point in – 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 Mv−metric to revisit the...

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

Publié en ligne: 26 déc. 2023

Pages: 272 - 287

Reçu: 22 déc. 2020

DOI: https://doi.org/10.2478/ausm-2023-0015

Mots clés
fixed point in ℳ–metric space and applications

© 2023 Meena Joshi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

Publié en ligne: 26 déc. 2023

Pages: 272 - 287

Reçu: 22 déc. 2020

DOI: https://doi.org/10.2478/ausm-2023-0015

Mots clésfixed point in ℳ–metric space and applications

© 2023 Meena Joshi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

Mots clés
fixed point in ℳ–metric space and applications