Abstract
AbstractIn this paper, we first introduce several new contractions by some auxiliary functions. Then we establish some φ-fixed point results for $(\gamma ,\psi ,\varphi ,\phi )$
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contractions, rational-$(\gamma , \psi ,\varphi ,\phi )$
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contractions and almost-$(\gamma ,\psi , \varphi ,\phi )$
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contractions and φ-fixed disc results for $(\psi ,\varphi ,\phi )_{x_{0}}$
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type 1 contractions, $(\psi ,\varphi ,\phi )_{x_{0}}$
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type 2 contractions, and $(\psi ,\varphi ,\phi )_{x_{0}}$
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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.
Funder
National Natural Science Foundation of China
Fundamental Research Funds for Central Universities of the Central South University
Zigong Science and Technology Program of China
the Opening Project of Key Laboratory of Higher Education of Sichuan Province for Enterprise Informationalization and Internet of Things
2020 Graduate Innovation Project of Sichuan University of Science and Engineering
2021 Innovation and Entrepreneurship Training Program for College Students of Sichuan University of Science and Engineering
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Cited by
1 articles.
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