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Volume 14
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10.3390/math14101757
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Relational Nonlinear Almost Contractions of Mukherjea Type and Applications to Boundary Value Problems

by
Doaa Filali
1,
Mohammed Zayed Alruwaytie
2,
Abdulaziz Abbas Alshammari
2,
Adel Alatawi
3,
Fahad M. Alamrani
3,* and
Faizan Ahmad Khan
3,*
1
Department of Mathematical Science, College of Sciences, Princess Nourah Bint Abdulrahman University, Riyadh 11671, Saudi Arabia
2
Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia
3
Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
*
Authors to whom correspondence should be addressed.
Mathematics 2026, 14(10), 1757; https://doi.org/10.3390/math14101757
Submission received: 8 April 2026 / Revised: 11 May 2026 / Accepted: 18 May 2026 / Published: 20 May 2026
Versions Notes

Abstract

In this paper, we explore specific fixed-point outcomes under a Mukherjea-Type nonlinear description of almost contractions in a metric space with a locally ℏ-transitive binary relation. Numerous previous insights are expanded, developed, improved, and consolidated in the outcomes reported herein. To demonstrate the reliability of our results, a couple of instances are supplied. Our outcomes are deployed to evaluate the accuracy of the unique solution of a boundary value problem.
Keywords: binary relations; fixed points; nonlinear almost contractions; boundary value problems binary relations; fixed points; nonlinear almost contractions; boundary value problems

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MDPI and ACS Style

Filali, D.; Alruwaytie, M.Z.; Alshammari, A.A.; Alatawi, A.; Alamrani, F.M.; Khan, F.A. Relational Nonlinear Almost Contractions of Mukherjea Type and Applications to Boundary Value Problems. Mathematics 2026, 14, 1757. https://doi.org/10.3390/math14101757

AMA Style

Filali D, Alruwaytie MZ, Alshammari AA, Alatawi A, Alamrani FM, Khan FA. Relational Nonlinear Almost Contractions of Mukherjea Type and Applications to Boundary Value Problems. Mathematics. 2026; 14(10):1757. https://doi.org/10.3390/math14101757

Chicago/Turabian Style

Filali, Doaa, Mohammed Zayed Alruwaytie, Abdulaziz Abbas Alshammari, Adel Alatawi, Fahad M. Alamrani, and Faizan Ahmad Khan. 2026. "Relational Nonlinear Almost Contractions of Mukherjea Type and Applications to Boundary Value Problems" Mathematics 14, no. 10: 1757. https://doi.org/10.3390/math14101757

APA Style

Filali, D., Alruwaytie, M. Z., Alshammari, A. A., Alatawi, A., Alamrani, F. M., & Khan, F. A. (2026). Relational Nonlinear Almost Contractions of Mukherjea Type and Applications to Boundary Value Problems. Mathematics, 14(10), 1757. https://doi.org/10.3390/math14101757

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