On the Admissibility of the Fixed Points Set of a Mapping with Respect to Another Mapping

Samet, Bessem

doi:10.3390/math9161981

Mathematics

2021

DOI: 10.3390/math9161981

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On the Admissibility of the Fixed Points Set of a Mapping with Respect to Another Mapping

Bessem Samet

Abstract: Let (M,δ) be a metric space, f:M→M, and g:M→[0,+∞). In this paper, we obtain sufficient conditions under which the set of fixed points of f is g-admissible, i.e., Fix(f)≠∅ and Fix(f)⊂g−10. Some special cases of our main results are discussed and some examples are given.

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

et al. 2022

View full text Add to dashboard Cite

show abstract

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On the Admissibility of the Fixed Points Set of a Mapping with Respect to Another Mapping

Abstract: Let (M,δ) be a metric space, f:M→M, and g:M→[0,+∞). In this paper, we obtain sufficient conditions under which the set of fixed points of f is g-admissible, i.e., Fix(f)≠∅ and Fix(f)⊂g−10. Some special cases of our main results are discussed and some examples are given.

Cited by 1 publication

References 22 publications

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

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

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