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

We propose 𝒮𝒜, η−𝒮𝒜, η−𝒮 𝒜min, and 𝒮𝒜η,δ,ζ−contractions and notions of η−admissibility type <italic>b</italic> and η<italic>b</italic>−regularity in parametric <italic>N</italic><italic>b</italic>-metric spaces to determine a unique fixed point, a unique fixed circle, and a greatest fixed disc. Further, we investigate the geometry of non-unique fixed points of a self mapping and demonstrate by illustrative examples that a circle or a disc in parametric <italic>N</italic><italic>b</italic>−metric space is not necessarily the same as a circle or a disc in a Euclidean space. Obtained outcomes are extensions, unifications, improvements, and generalizations of some of the well-known previous results. We provide non-trivial illustrations to exhibit the importance of our explorations. Towards the end, we resolve the system of linear equations to demonstrate the significance of our contractions in parametric <italic>N</italic><italic>b</italic>−metric space.
</abstract>

We propose 𝒮𝒜, η−𝒮𝒜, η−𝒮 𝒜min, and 𝒮𝒜η,δ,ζ−contractions and notions of η−admissibility type b and ηb−regularity in parametric Nb-metric spaces to determine a unique fixed point, a unique fixed circle, and a greatest fixed disc. Further, we investigate the geometry of non-unique fixed points of a self mapping and demonstrate by illustrative examples that a circle or a disc in parametric Nb−metric space is not necessarily the same as a circle or a disc in a Euclidean space. Obtained outcomes are extensions, unifications, improvements, and generalizations of some of the well-known previous results. We provide non-trivial illustrations to exhibit the importance of our explorations. Towards the end, we resolve the system of linear equations to demonstrate the significance of our contractions in parametric Nb−metric space.

On unique and non-unique fixed point in parametric <italic>N</italic><italic>b</italic><italic>−</italic>metric spaces with application

Pt. L. M. S. Campus, Sridev Suman Uttarakhand University

S. S. J. Campus, Soban Singh Jeena, Uttarakhand University

Acta Universitatis Sapientiae, Mathematica

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

On unique and non-unique fixed point in parametric metric spaces with application

We propose 𝒮𝒜, η−𝒮𝒜, η−𝒮 𝒜min, and 𝒮𝒜η,δ,ζ−contractions and notions of η−admissibility type b and ηb−regularity in parametric Nb-metric spaces to...

On unique and non-unique fixed point in parametric N_b−metric spaces with application

Published Online: Jan 19, 2023

Page range: 278 - 307

Received: Dec 22, 2020

DOI: https://doi.org/10.2478/ausm-2022-0019

Keywords
continuity, completeness, η−admissible type b, η−regular, fixed circle

© 2022 Sudheer Petwal et al., published by Sciendo

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

On unique and non-unique fixed point in parametric Nb−metric spaces with application

Published Online: Jan 19, 2023

Page range: 278 - 307

Received: Dec 22, 2020

DOI: https://doi.org/10.2478/ausm-2022-0019

Keywordscontinuity, completeness, η−admissible type b, η−regular, fixed circle

© 2022 Sudheer Petwal et al., published by Sciendo

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

On unique and non-unique fixed point in parametric N_b−metric spaces with application

Keywords
continuity, completeness, η−admissible type b, η−regular, fixed circle