Some new φ-fixed point and φ-fixed disc results via auxiliary functions
Abstract In this paper, we first introduce several new contractions by some auxiliary functions. Then we establish some φ-fixed point results for ( γ , ψ , φ , ϕ ) $(\gamma ,\psi ,\varphi ,\phi )$ contractions, rational- ( γ , ψ , φ , ϕ ) $(\gamma , \psi ,\varphi ,\phi )$ contractions and almost- (...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-09-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-022-02852-7 |
| _version_ | 1811211659704795136 |
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| author | Yan Sun Xiao-lan Liu Jia Deng Mi Zhou Huan Zhang |
| author_facet | Yan Sun Xiao-lan Liu Jia Deng Mi Zhou Huan Zhang |
| author_sort | Yan Sun |
| collection | DOAJ |
| description | Abstract In this paper, we first introduce several new contractions by some auxiliary functions. Then we establish some φ-fixed point results for ( γ , ψ , φ , ϕ ) $(\gamma ,\psi ,\varphi ,\phi )$ contractions, rational- ( γ , ψ , φ , ϕ ) $(\gamma , \psi ,\varphi ,\phi )$ contractions and almost- ( γ , ψ , φ , ϕ ) $(\gamma ,\psi , \varphi ,\phi )$ contractions and φ-fixed disc results for ( ψ , φ , ϕ ) x 0 $(\psi ,\varphi ,\phi )_{x_{0}}$ type 1 contractions, ( ψ , φ , ϕ ) x 0 $(\psi ,\varphi ,\phi )_{x_{0}}$ type 2 contractions, and ( ψ , φ , ϕ ) x 0 $(\psi ,\varphi ,\phi )_{x_{0}}$ 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. |
| first_indexed | 2024-04-12T05:16:22Z |
| format | Article |
| id | doaj.art-ccae01e1dfa442169f6289b46370c7cf |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-12T05:16:22Z |
| publishDate | 2022-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-ccae01e1dfa442169f6289b46370c7cf2022-12-22T03:46:37ZengSpringerOpenJournal of Inequalities and Applications1029-242X2022-09-012022112610.1186/s13660-022-02852-7Some new φ-fixed point and φ-fixed disc results via auxiliary functionsYan Sun0Xiao-lan Liu1Jia Deng2Mi Zhou3Huan Zhang4College of Mathematics and Statistics, Sichuan University of Science and EngineeringCollege of Mathematics and Statistics, Sichuan University of Science and EngineeringCollege of Mathematics and Statistics, Sichuan University of Science and EngineeringSchool of Science and Techology, University of SanyaCollege of Mathematics and Statistics, Sichuan University of Science and EngineeringAbstract In this paper, we first introduce several new contractions by some auxiliary functions. Then we establish some φ-fixed point results for ( γ , ψ , φ , ϕ ) $(\gamma ,\psi ,\varphi ,\phi )$ contractions, rational- ( γ , ψ , φ , ϕ ) $(\gamma , \psi ,\varphi ,\phi )$ contractions and almost- ( γ , ψ , φ , ϕ ) $(\gamma ,\psi , \varphi ,\phi )$ contractions and φ-fixed disc results for ( ψ , φ , ϕ ) x 0 $(\psi ,\varphi ,\phi )_{x_{0}}$ type 1 contractions, ( ψ , φ , ϕ ) x 0 $(\psi ,\varphi ,\phi )_{x_{0}}$ type 2 contractions, and ( ψ , φ , ϕ ) x 0 $(\psi ,\varphi ,\phi )_{x_{0}}$ 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.https://doi.org/10.1186/s13660-022-02852-7φ-fixed pointφ-fixed disc( γ , ψ , φ , ϕ ) $(\gamma ,\psi ,\varphi ,\phi )$ contraction( ψ , φ , ϕ ) x 0 $(\psi ,\varphi ,\phi )_{x_{0}}$ contractionNonlinear integral equations |
| spellingShingle | Yan Sun Xiao-lan Liu Jia Deng Mi Zhou Huan Zhang Some new φ-fixed point and φ-fixed disc results via auxiliary functions Journal of Inequalities and Applications φ-fixed point φ-fixed disc ( γ , ψ , φ , ϕ ) $(\gamma ,\psi ,\varphi ,\phi )$ contraction ( ψ , φ , ϕ ) x 0 $(\psi ,\varphi ,\phi )_{x_{0}}$ contraction Nonlinear integral equations |
| title | Some new φ-fixed point and φ-fixed disc results via auxiliary functions |
| title_full | Some new φ-fixed point and φ-fixed disc results via auxiliary functions |
| title_fullStr | Some new φ-fixed point and φ-fixed disc results via auxiliary functions |
| title_full_unstemmed | Some new φ-fixed point and φ-fixed disc results via auxiliary functions |
| title_short | Some new φ-fixed point and φ-fixed disc results via auxiliary functions |
| title_sort | some new φ fixed point and φ fixed disc results via auxiliary functions |
| topic | φ-fixed point φ-fixed disc ( γ , ψ , φ , ϕ ) $(\gamma ,\psi ,\varphi ,\phi )$ contraction ( ψ , φ , ϕ ) x 0 $(\psi ,\varphi ,\phi )_{x_{0}}$ contraction Nonlinear integral equations |
| url | https://doi.org/10.1186/s13660-022-02852-7 |
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