Best proximity points for proximal Górnicki mappings and applications to variational inequality problems

P. Dhivya; D. Diwakaran; P. Selvapriya; P. Dhivya; D. Diwakaran; P. Selvapriya

doi:10.3934/math.2024287

AIMS Mathematics

2024, Volume 9, Issue 3: 5886-5904. doi: 10.3934/math.2024287

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Research article

Best proximity points for proximal Górnicki mappings and applications to variational inequality problems

Department of Mathematics, Vellore Institute of Technology, Chennai-600 127, India

Received: 16 November 2023 Revised: 18 December 2023 Accepted: 27 December 2023 Published: 31 January 2024
MSC : 47H05, 47H10, 54J25

We introduce a large class of mappings called proximal Górnicki mappings in metric spaces, which includes Górnicki mappings, enriched Kannan mappings, enriched Chatterjea mappings, and enriched mappings. We prove the existence of the best proximity points in metric spaces and partial metric spaces. Moreover, we utilize appropriate examples to illustrate our results, and we verify the convergence behavior. As an application of our result, we prove the existence and uniqueness of a solution for the variational inequality problems. The obtained results generalize the existing results in the literature.
- fixed points,
- best proximity points,
- Górnicki mapping,
- enriched contraction,
- partial metric space,
- variational inequality
Citation: P. Dhivya, D. Diwakaran, P. Selvapriya. Best proximity points for proximal Górnicki mappings and applications to variational inequality problems[J]. AIMS Mathematics, 2024, 9(3): 5886-5904. doi: 10.3934/math.2024287

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Abstract

We introduce a large class of mappings called proximal Górnicki mappings in metric spaces, which includes Górnicki mappings, enriched Kannan mappings, enriched Chatterjea mappings, and enriched mappings. We prove the existence of the best proximity points in metric spaces and partial metric spaces. Moreover, we utilize appropriate examples to illustrate our results, and we verify the convergence behavior. As an application of our result, we prove the existence and uniqueness of a solution for the variational inequality problems. The obtained results generalize the existing results in the literature.

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