On a class of fixed points for set contractions on partial metric spaces with a digraph

Talat Nazir; Zakaria Ali; Shahin Nosrat Jogan; Manuel de la Sen; Talat Nazir; Zakaria Ali; Shahin Nosrat Jogan; Manuel de la Sen

doi:10.3934/math.2023065

AIMS Mathematics

2023, Volume 8, Issue 1: 1304-1328. doi: 10.3934/math.2023065

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On a class of fixed points for set contractions on partial metric spaces with a digraph

1.
Department of Mathematical Sciences, University of South Africa, Florida 0003, South Africa
2.
Institute of Research and Development of Processes, University of the Basque Country, Leioa 48940, Bizkaia, Spain

Received: 27 July 2022 Revised: 07 October 2022 Accepted: 10 October 2022 Published: 19 October 2022
MSC : 47H04, 47H07, 47H10

We investigate the existence of fixed point problems on a partial metric space. The results obtained are for set contractions in the domain of sets and the pattern for the partial metric space is constructed on a directed graph. Essentially, our main strategy is to employ generalized $ \phi $-contractions in order to prove our results, where the fixed points are investigated with a graph structure. Moreover, we state and prove the well-posedness of fixed point based problems of the generalized $ \phi $-contractive operator in the framework of a partial metric space. We illustrate the main results in this manuscript by providing several examples.
- fixed point,
- set-contraction,
- partial metric space,
- graph,
- graph contraction
Citation: Talat Nazir, Zakaria Ali, Shahin Nosrat Jogan, Manuel de la Sen. On a class of fixed points for set contractions on partial metric spaces with a digraph[J]. AIMS Mathematics, 2023, 8(1): 1304-1328. doi: 10.3934/math.2023065

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Abstract

We investigate the existence of fixed point problems on a partial metric space. The results obtained are for set contractions in the domain of sets and the pattern for the partial metric space is constructed on a directed graph. Essentially, our main strategy is to employ generalized $ \phi $-contractions in order to prove our results, where the fixed points are investigated with a graph structure. Moreover, we state and prove the well-posedness of fixed point based problems of the generalized $ \phi $-contractive operator in the framework of a partial metric space. We illustrate the main results in this manuscript by providing several examples.

References

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