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Discontinuity, Nonlinearity, and Complexity 12(3) (2023) 469--483 | DOI:10.5890/DNC.2023.09.001

Jia Deng$^{1}$, Xiao-lan Liu$^{1,2,3}$, Yan Sun$^{1}$

$^1$ College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, China

$^2$ Artificial Intelligence Key Laboratory of Sichuan Province, Zigong, Sichuan 643000, China

$^3$ South Sichuan Center for Applied Mathematics, Zigong, Sichuan 643000, China

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Abstract

In this article, we present several types of generalized $\alpha$-admissible almost type $\mathcal{Z}$-contractions, which can be considered as the generalizations of $\alpha$-admissible $\mathcal{Z}$-contractions and almost $\mathcal{Z}$-contractions, and obtain the fixed point results of these contractions in complete metric spaces. Moreover, we utilize some examples to verify the validity of main results. Finally, we give some fixed point results related to our results.

Acknowledgments

This work is partially supported by National Natural Science Foundation of China(Grant No.11872043), Natural Science Foundation of Sichuan Province (Grant No.2023NSFSC1299), Fund Project of Sichuan University of Science and Engineering in hit-haunting for talents (Grant No.2022RC04), 2021 Innovation and Entrepreneurship Training Program for College Students of Sichuan University of Science and Engineering (Grant No.cx2021150), 2022 Graduate Innovation Project of Sichuan University of Science and Engineering (Grant No.Y2022190).

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