Proinov-type relational contractions and applications to boundary value problems

Abdul Wasey; Wan Ainun Mior Othman; Esmail Alshaban; Kok Bin Wong; Adel Alatawi; Abdul Wasey; Wan Ainun Mior Othman; Esmail Alshaban; Kok Bin Wong; Adel Alatawi

doi:10.3934/math.2025601

AIMS Mathematics

2025, Volume 10, Issue 6: 13393-13408. doi: 10.3934/math.2025601

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Research article

Proinov-type relational contractions and applications to boundary value problems

1.
Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, 50603 Kuala Lumpur, Malaysia
2.
Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia

Received: 14 January 2025 Revised: 07 May 2025 Accepted: 16 May 2025 Published: 11 June 2025
MSC : 34B15, 47H10, 54H25

This manuscript deals with proving certain metrical fixed-point findings for a class of generalized contractions involving a couple $ (\psi, \varphi) $ of test functions employing a local class of transitive relation. The outcomes investigated herein refine, modify, unify, and sharpen various existing outcomes. To attest the accuracy of our outcomes, we provide a few examples. By means of our outcomes, we impart an explanation of the reality of a solution to a boundary value problem.
- fixed points,
- Picard sequence,
- $ \textbf{S} $-completeness,
- locally transitive relation,
- upper and lower solutions
Citation: Abdul Wasey, Wan Ainun Mior Othman, Esmail Alshaban, Kok Bin Wong, Adel Alatawi. Proinov-type relational contractions and applications to boundary value problems[J]. AIMS Mathematics, 2025, 10(6): 13393-13408. doi: 10.3934/math.2025601

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Abstract

This manuscript deals with proving certain metrical fixed-point findings for a class of generalized contractions involving a couple $ (\psi, \varphi) $ of test functions employing a local class of transitive relation. The outcomes investigated herein refine, modify, unify, and sharpen various existing outcomes. To attest the accuracy of our outcomes, we provide a few examples. By means of our outcomes, we impart an explanation of the reality of a solution to a boundary value problem.

References

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