Fixed point theorems for weakly compatible mappings under implicit relations in quaternion valued $G$-metric spaces

Mohamed Gamal; Watcharaporn Cholamjiak; Mohamed Gamal; Watcharaporn Cholamjiak

doi:10.3934/math.2021125

AIMS Mathematics

2021, Volume 6, Issue 3: 2048-2058. doi: 10.3934/math.2021125

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Research article

Fixed point theorems for weakly compatible mappings under implicit relations in quaternion valued $G$-metric spaces

Mohamed Gamal ¹,
Watcharaporn Cholamjiak ^{2
,
,}

1.
Department of Mathematics, Faculty of Science, South Valley University, Luxor 85844, Egypt
2.
School of Science, University of Phayao, Phayao, 56000, Thailand

Received: 04 August 2020 Accepted: 16 November 2020 Published: 08 December 2020
MSC : 47H10, 55H02

In this paper, we established some common fixed point theorems of four self-mappings in completed quaternion valued $G-$metric space. Moreover, we gave an example of completed quaternion valued $G-$metric space and example for supporting our main results. The results obtained in this paper extend and improve some recent results.
- quaternion valued $G-$metric space,
- common fixed point,
- weakly compatible mapping,
- implicit relation,
- coincident point
Citation: Mohamed Gamal, Watcharaporn Cholamjiak. Fixed point theorems for weakly compatible mappings under implicit relations in quaternion valued $G$-metric spaces[J]. AIMS Mathematics, 2021, 6(3): 2048-2058. doi: 10.3934/math.2021125

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Abstract

In this paper, we established some common fixed point theorems of four self-mappings in completed quaternion valued $G-$metric space. Moreover, we gave an example of completed quaternion valued $G-$metric space and example for supporting our main results. The results obtained in this paper extend and improve some recent results.

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