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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.

References

1. [1]	Banach, S. (1922), Sur les o{p}erations dans les ensembles abstraits et leur application aux équations intégrales, Fundamenta Mathematicae, 3(1), 133-181.

2. [2]	Khojasteh, F., Shukla, S., and Redenovi, S. (2015), A new approach to the study fixed point theorems via simulation functions, Filomat, 29(6), 1189-1194.

3. [3]	Nastasi, A. and Vetro, P. (2015), Fixed point results on metric and partial metric spaces via simulation functions, Journal of Nonlinear Science and Applications, 8(6), 1059-1069.

4. [4]	Karapinar, E. (2016), Fixed points results via simulation functions, Filomat, 30(8), 2343-2350.

5. [5]	Isik, H., Gungor, N.B., Park, C., and Jang, S.Y. (2018), Fixed point theorems for almost $\mathcal{Z}$-contractions with an application, Mathematics, 6(3), 27.

6. [6]	Cvetkovi, M., Karapinar, E., and Rakoevi, V. (2018), Fixed point results for admissible $\mathcal{Z}$-contractions, Fixed Point Theory, 19(2), 515-526.

7. [7]	Alghamdi, M.A., Gulyaz-Ozyurt, S., and Karapinar, E. (2020), A note on extended $\mathcal{Z}$-contraction, Mathematics, 8(2), 195.

8. [8]	Kumar, M. and Sharma, R. (2019), A new approach to the study of fixed point theory for simulation functions in $G$-metric spaces, Boletim da Sociedade Paranaense de Matematica, 37(2), 115-121.

9. [9]	Chifu, C. and Karapinar, E. (2020), On contractions via simulation functions on extended $b$-metric spaces, Miskolc Mathematical Notes, 21(1), 127-141.

10. [10]	Chifu, C. and Karapinar, E. (2019), Admissible hybrid $\mathcal{Z}$-contractions in $b$-metric spaces, Axioms, 9(1), 2.

11. [11]	Samet, B., Vetro, C., and Vetro, P. (2012), Fixed point theorems for $\alpha$-$\psi$-contractive type mappings, Nonlinear Analysis: Theory, Methods and Applications, 75(4), 2154-2165.

12. [12]	Karapinar, E., Kumam, P., and Salimi, P. (2013), On $\alpha$-$\psi$-Meir-Keeler contractive mappings, Fixed Point Theory and Applications, 2013, 94.

13. [13]	Popescu, O. (2014), Some new fixed point theorems for $\alpha$-Geraghty contraction type maps in metric spaces, Fixed Point Theory and Applications, 2014, 190.

14. [14]	Radenovic, S., Kadelburg, Z., Jandrlic, D., and Jandrlic, A. (2012), Some results on weakly contractive maps, Bulletin of the Iranian Mathematical Society, 38(3), 625-645.