Common fixed point results via $ \mathcal{A}_{\vartheta} $-$ \alpha $-contractions with a pair and two pairs of self-mappings in the frame of an extended quasi $ b $-metric space

Amina-Zahra Rezazgui; Abdalla Ahmad Tallafha; Wasfi Shatanawi; Amina-Zahra Rezazgui; Abdalla Ahmad Tallafha; Wasfi Shatanawi

doi:10.3934/math.2023363

AIMS Mathematics

2023, Volume 8, Issue 3: 7225-7241. doi: 10.3934/math.2023363

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Common fixed point results via $ \mathcal{A}_{\vartheta} $-$ \alpha $-contractions with a pair and two pairs of self-mappings in the frame of an extended quasi $ b $-metric space

1.
Department of Mathematics, Faculty of Science, University of Jordan, Amman, Jordan
2.
Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia
3.
Medical Research, China Medical University Hospital, China Medical University, Taichung
4.
Department of Mathematics, Faculty of Science, Hashemite University, Zarqa, Jordan

Received: 07 October 2022 Revised: 22 December 2022 Accepted: 30 December 2022 Published: 12 January 2023
MSC : 37C25, 47H10, 54H25

In this paper, we take advantage of implicit relationships to come up with a new concept called "$ \mathcal{A}_{\vartheta} $-$ \alpha $-contraction mapping". We utilized our new notion to formulate and prove some common fixed point theorems for two and four self-mappings over complete extended quasi $ b $-metric spaces under a set of conditions. Our main results widen and improve many existing results in the literature. To support our research, we present some examples as applications to our main findings.
- common fixed point,
- extended quasi $ b $-metric space,
- $ \mathcal{A}_{\vartheta} $-$ \alpha $-contractions,
- compatible mapping
Citation: Amina-Zahra Rezazgui, Abdalla Ahmad Tallafha, Wasfi Shatanawi. Common fixed point results via $ \mathcal{A}_{\vartheta} $-$ \alpha $-contractions with a pair and two pairs of self-mappings in the frame of an extended quasi $ b $-metric space[J]. AIMS Mathematics, 2023, 8(3): 7225-7241. doi: 10.3934/math.2023363

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Abstract

In this paper, we take advantage of implicit relationships to come up with a new concept called "$ \mathcal{A}_{\vartheta} $-$ \alpha $-contraction mapping". We utilized our new notion to formulate and prove some common fixed point theorems for two and four self-mappings over complete extended quasi $ b $-metric spaces under a set of conditions. Our main results widen and improve many existing results in the literature. To support our research, we present some examples as applications to our main findings.

References

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