2022
DOI: 10.2478/ausm-2022-0019
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On unique and non-unique fixed point in parametric N b metric spaces with application

Abstract: We propose 𝒮𝒜, η−𝒮𝒜, η−𝒮 𝒜min, and 𝒮𝒜η,δ,ζ−contractions and notions of η−admissibility type b and η b −regularity in parametric N b -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 N … Show more

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Cited by 3 publications
(1 citation statement)
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“…However, the reverse implication may not hold. Following the pattern of Theorem 3.27, we can also establish the uniqueness of fixed circle using ω$$ \omega $$ψ$$ \psi $$‐interpolative Suzuki‐ Kannan type contraction, ω$$ \omega $$ψ$$ \psi $$‐interpolative Suzuki–Ćirić–Reich–Rus type contraction and other interpolative contractions. For details on the work on the set of non‐unique fixed points forming some fixed figure one may refer to literature, 6,21,38,41–45 and references therein.…”
Section: Resultsmentioning
confidence: 99%
“…However, the reverse implication may not hold. Following the pattern of Theorem 3.27, we can also establish the uniqueness of fixed circle using ω$$ \omega $$ψ$$ \psi $$‐interpolative Suzuki‐ Kannan type contraction, ω$$ \omega $$ψ$$ \psi $$‐interpolative Suzuki–Ćirić–Reich–Rus type contraction and other interpolative contractions. For details on the work on the set of non‐unique fixed points forming some fixed figure one may refer to literature, 6,21,38,41–45 and references therein.…”
Section: Resultsmentioning
confidence: 99%