On fixed point theorems for ordered contractions with applications

Zili Shi; Huaping Huang; Bessem Samet; Yuxin Wang; Zili Shi; Huaping Huang; Bessem Samet; Yuxin Wang

doi:10.3934/math.2025238

AIMS Mathematics

2025, Volume 10, Issue 3: 5173-5196. doi: 10.3934/math.2025238

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On fixed point theorems for ordered contractions with applications

1.
School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404020, China
2.
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia

Received: 29 December 2024 Revised: 26 February 2025 Accepted: 28 February 2025 Published: 07 March 2025
MSC : 54H25, 47H10, 54E50

The purpose of this paper is to prove some fixed point theorems for ordered contractions in partially ordered $ b $-metric spaces. We consider several common fixed point and coincidence point results for four mappings in such spaces. The results obtained in this paper significantly extend numerous results in the existing literature. Further, we present some supportive examples to emphasize the potential value of our results. In addition, as applications, we verify the existence and uniqueness of solutions to a large number of equations.
- common fixed point,
- coincidence point,
- $ b $-metric space,
- ordered contractive pair,
- weakly compatible
Citation: Zili Shi, Huaping Huang, Bessem Samet, Yuxin Wang. On fixed point theorems for ordered contractions with applications[J]. AIMS Mathematics, 2025, 10(3): 5173-5196. doi: 10.3934/math.2025238

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Abstract

The purpose of this paper is to prove some fixed point theorems for ordered contractions in partially ordered $ b $-metric spaces. We consider several common fixed point and coincidence point results for four mappings in such spaces. The results obtained in this paper significantly extend numerous results in the existing literature. Further, we present some supportive examples to emphasize the potential value of our results. In addition, as applications, we verify the existence and uniqueness of solutions to a large number of equations.

References

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