Fixed point results for a new $ \alpha $-$ \theta $-Geraghty type contraction mapping in metric-like space via $ \mathcal{C}_\mathcal{G} $-simulation functions

Abdellah Taqbibt; M'hamed Elomari; Milica Savatović; Said Melliani; Stojan Radenović; Abdellah Taqbibt; M'hamed Elomari; Milica Savatović; Said Melliani; Stojan Radenović

doi:10.3934/math.20231548

AIMS Mathematics

2023, Volume 8, Issue 12: 30313-30334. doi: 10.3934/math.20231548

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Fixed point results for a new $ \alpha $-$ \theta $-Geraghty type contraction mapping in metric-like space via $ \mathcal{C}_\mathcal{G} $-simulation functions

1.
Laboratory of Applied Mathematics and Scientific Calculus, Sultan Moulay Slimane University, P.O. Box 523, FST, Beni Mellal, 23000, Morocco
2.
School of Electrical Engineering, University of Belgrade, Bulevar kralja Aleksandra 73, Belgrade, 11120, Serbia
3.
Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, Belgrade, 11120, Serbia

Received: 17 August 2023 Revised: 19 October 2023 Accepted: 23 October 2023 Published: 08 November 2023
MSC : 47H10, 37C25, 47H09

This paper aims to introduce the new concept of an $ \alpha $-$ \theta $-Geraghty type contraction mapping using $ \mathcal{C}_{\mathcal{G}} $-simulation in a metric-like space. Additionally, through this type of contraction, we establish fixed point results that generalize several known fixed point results in the literature. We provide some examples as an application that proves the credibility of our results.
- metric-like space,
- fixed point,
- Geraghty contraction,
- ($ \alpha, \theta $)-admissible mapping,
- $ \mathcal{C}_{\mathcal{G}} $-simulation function
Citation: Abdellah Taqbibt, M'hamed Elomari, Milica Savatović, Said Melliani, Stojan Radenović. Fixed point results for a new $ \alpha $-$ \theta $-Geraghty type contraction mapping in metric-like space via $ \mathcal{C}_\mathcal{G} $-simulation functions[J]. AIMS Mathematics, 2023, 8(12): 30313-30334. doi: 10.3934/math.20231548

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Abstract

This paper aims to introduce the new concept of an $ \alpha $-$ \theta $-Geraghty type contraction mapping using $ \mathcal{C}_{\mathcal{G}} $-simulation in a metric-like space. Additionally, through this type of contraction, we establish fixed point results that generalize several known fixed point results in the literature. We provide some examples as an application that proves the credibility of our results.

References

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