Meir–Keeler Type Contraction in Orthogonal M-Metric Spaces
Abstract
:1. Introduction
2. Preliminaries
3. Main Results
- (i)
- ,
- (ii)
- .
- (i)
- (ii)
- (iii)
- (iv)
- such that for all with , we have
- (a)
- a sequence
- (b)
- sequence is called -Cauchy sequence if
- (c)
- if for every -Cauchy sequence such that
- (i)
- If and , then and ;
- (ii)
- If and , then ;
- (iii)
- If and , then and ;
- (iv)
- If and , then and .
4. Fixed Points for Integral Type Contractions
- (i)
- ,
- (ii)
- h is non-decreasing and right continuous,
- (iii)
- for every , there exists such that
- (i)
- ;
- (ii)
- and for each , satisfying
- (i)
- O is continuous and non-decreasing,
- (ii)
- and .
5. Applications
- (i)
- is continous and ;
- (ii)
- and is increasing for all ;
- (iii)
- for all and , we have
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Alsaadi, A.; Singh, B.; Singh, V.; Uddin, I. Meir–Keeler Type Contraction in Orthogonal M-Metric Spaces. Symmetry 2022, 14, 1856. https://doi.org/10.3390/sym14091856
Alsaadi A, Singh B, Singh V, Uddin I. Meir–Keeler Type Contraction in Orthogonal M-Metric Spaces. Symmetry. 2022; 14(9):1856. https://doi.org/10.3390/sym14091856
Chicago/Turabian StyleAlsaadi, Ateq, Bijender Singh, Vizender Singh, and Izhar Uddin. 2022. "Meir–Keeler Type Contraction in Orthogonal M-Metric Spaces" Symmetry 14, no. 9: 1856. https://doi.org/10.3390/sym14091856
APA StyleAlsaadi, A., Singh, B., Singh, V., & Uddin, I. (2022). Meir–Keeler Type Contraction in Orthogonal M-Metric Spaces. Symmetry, 14(9), 1856. https://doi.org/10.3390/sym14091856