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/lp/de-gruyter/on-unique-and-non-unique-fixed-point-in-parametric-nb-metric-spaces-8WawkMmW8c
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- Publisher
- de Gruyter
- Copyright
- © 2022 Sudheer Petwal et al., published by Sciendo
- eISSN
- 2066-7752
- DOI
- 10.2478/ausm-2022-0019
- Publisher site
- See Article on Publisher Site
Abstract
AbstractWe 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.
Journal
Acta Universitatis Sapientiae, Mathematica – de Gruyter
Published: Dec 1, 2022
Keywords: continuity; completeness; η−admissible type b; η b −regular; fixed circle; 47H10; 54H25; 47H09