Relation-Theoretic Nonlinear Almost Contractions with an Application to Boundary Value Problems
Abstract
:1. Introduction
2. Preliminaries
- (i)
- ;
- (ii)
- .
- (i)
- ;
- (ii)
3. Main Results
- (a)
- remains Λ-complete MS;
- (b)
- verifying ;
- (c)
- Λ is -closed;
- (d)
- serves as Λ-continuous or Λ remains ζ-self-closed;
- (e)
- ∃ and verifying
- (i)
- ∃ and verifies
- (ii)
- is -directed,
4. Illustrative Examples
5. An Application to BVP
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
MS | Metric space |
BCP | Banach contraction principle |
BVP | Boundary value problem |
iff | If and only if |
The set of natural numbers | |
The class of all real-valued continuous functions on a set A | |
The class of all real-valued continuously differentiable functions on a set A |
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Aljawi, S.; Uddin, I. Relation-Theoretic Nonlinear Almost Contractions with an Application to Boundary Value Problems. Mathematics 2024, 12, 1275. https://doi.org/10.3390/math12091275
Aljawi S, Uddin I. Relation-Theoretic Nonlinear Almost Contractions with an Application to Boundary Value Problems. Mathematics. 2024; 12(9):1275. https://doi.org/10.3390/math12091275
Chicago/Turabian StyleAljawi, Salma, and Izhar Uddin. 2024. "Relation-Theoretic Nonlinear Almost Contractions with an Application to Boundary Value Problems" Mathematics 12, no. 9: 1275. https://doi.org/10.3390/math12091275
APA StyleAljawi, S., & Uddin, I. (2024). Relation-Theoretic Nonlinear Almost Contractions with an Application to Boundary Value Problems. Mathematics, 12(9), 1275. https://doi.org/10.3390/math12091275