A study of common fixed points that belong to zeros of a certain given function with applications

Saleh, Hayel N.; Imdad, Mohammad; Karapınar, Erdal

doi:10.15388/namc.2021.26.21945

Cited by 2 publications

(1 citation statement)

References 14 publications

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“…A ϕ-fixed point is a fixed point of a mapping T such that it is also a zero of a given function ϕ (see [8] for more details). Then, ϕ-fixed point results for self-mappings defined in metric or generalized metric spaces have been intensively studied using different approaches (for example, see [18], [16] and the reference therein). In [16], an open problem concerning to the geometric properties of non-unique ϕ-fixed points have been considered.…”

Section: Suzuki Type Z C -Contractions and The Fixed-figure Problemmentioning

confidence: 99%

Suzuki type $\mathcal{Z}_{c}$-contraction mappings and the fixed-figure problem

Gopal,

Özgür,

Savaliya

et al. 2024

Hacettepe Journal of Mathematics and Statistics

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Geometric approaches are important for the study of some real-life problems. In metric fixed point theory, a recent problem called \textquotedblleft \textit{fixed-figure problem}\textquotedblright\ is the investigation of the existence of self-mapping which remain invariant at each points of a certain geometric figure (e.g. a circle, an ellipse and a Cassini curve) in the space. This problem is well studied in the domain of the extension of this line of research in the context of fixed circle, fixed disc, fixed ellipse, fixed Cassini curve and so on. In this paper, we introduce the concept of a Suzuki type $\mathcal{Z}_c$-contraction. We deal with the fixed-figure problem by means of the notions of a $\mathcal{Z}_c$-contraction and a Suzuki type $\mathcal{Z}_c$-contraction. We derive new fixed-figure results for the fixed ellipse and fixed Cassini curve cases by means of these notions. Also fixed disc and fixed circle results given for Suzuki type $\mathcal{Z}_c$-contraction. There are couple of illustration related to the obtained theoretical results.

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Section: Suzuki Type Z C -Contractions and The Fixed-figure Problemmentioning

confidence: 99%

Suzuki type $\mathcal{Z}_{c}$-contraction mappings and the fixed-figure problem

Gopal,

Özgür,

Savaliya

et al. 2024

Hacettepe Journal of Mathematics and Statistics

View full text Add to dashboard Cite

show abstract

Some new φ-fixed point and φ-fixed disc results via auxiliary functions

et al. 2022

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In this paper, we first introduce several new contractions by some auxiliary functions. Then we establish some φ-fixed point results for $(\gamma ,\psi ,\varphi ,\phi )$ ( γ , ψ , φ , ϕ ) contractions, rational-$(\gamma , \psi ,\varphi ,\phi )$ ( γ , ψ , φ , ϕ ) contractions and almost-$(\gamma ,\psi , \varphi ,\phi )$ ( γ , ψ , φ , ϕ ) contractions and φ-fixed disc results for $(\psi ,\varphi ,\phi )_{x_{0}}$ ( ψ , φ , ϕ ) x 0 type 1 contractions, $(\psi ,\varphi ,\phi )_{x_{0}}$ ( ψ , φ , ϕ ) x 0 type 2 contractions, and $(\psi ,\varphi ,\phi )_{x_{0}}$ ( ψ , φ , ϕ ) x 0 type 3 contractions in metric spaces. We generalize some existing φ-fixed point and φ-fixed circle results in the literature. Further, we give some examples to demonstrate the usefulness of our results and investigate the existence and uniqueness of solutions of nonlinear integral equations.

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A study of common fixed points that belong to zeros of a certain given function with applications

Cited by 2 publications

References 14 publications

Suzuki type $\mathcal{Z}_{c}$-contraction mappings and the fixed-figure problem

Suzuki type $\mathcal{Z}_{c}$-contraction mappings and the fixed-figure problem

Some new φ-fixed point and φ-fixed disc results via auxiliary functions

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