On Maia type fixed point results via implicit relation

Ashis Bera; Pratikshan Mondal; Hiranmoy Garai; Lakshmi Kanta Dey; Ashis Bera; Pratikshan Mondal; Hiranmoy Garai; Lakshmi Kanta Dey

doi:10.3934/math.20231124

AIMS Mathematics

2023, Volume 8, Issue 9: 22067-22080. doi: 10.3934/math.20231124

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On Maia type fixed point results via implicit relation

1.
Department of Mathematics, Vellore Institute Technology Chennai, India
2.
Department of Mathematics, Durgapur Government College, Durgapur, India
3.
Department of Science and Humanities, Siliguri Govt. Polytechnic, Siliguri, India
4.
Department of Mathematics, National Institute of Technology Durgapur, India

Received: 19 February 2023 Revised: 18 May 2023 Accepted: 05 June 2023 Published: 12 July 2023
MSC : 47H10, 54H25

In order to study Maia type fixed point results for several well-known contractions, we suggest two novel contractions called $ \mathcal{A} $-contraction and $ \mathcal{A}' $-contraction. The majority of the Maia type fixed point results for various contractions can now be unified through these, which eliminate the need to manage various contractions individually. The advantage of including such contractions in the study of Maia type fixed point results has been demonstrated in suitable examples. We present an application of one of our established results towards the conclusion of the paper.
- metric space,
- fixed point,
- $ \mathcal{A} $-contractions,
- $ \mathcal{A}' $-contraction,
- enriched contractions
Citation: Ashis Bera, Pratikshan Mondal, Hiranmoy Garai, Lakshmi Kanta Dey. On Maia type fixed point results via implicit relation[J]. AIMS Mathematics, 2023, 8(9): 22067-22080. doi: 10.3934/math.20231124

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Abstract

In order to study Maia type fixed point results for several well-known contractions, we suggest two novel contractions called $ \mathcal{A} $-contraction and $ \mathcal{A}' $-contraction. The majority of the Maia type fixed point results for various contractions can now be unified through these, which eliminate the need to manage various contractions individually. The advantage of including such contractions in the study of Maia type fixed point results has been demonstrated in suitable examples. We present an application of one of our established results towards the conclusion of the paper.

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