Fixed Point Results via Orthogonal (α − 𝔶 − 𝔾)-Contraction in Orthogonal Complete Metric Space
Abstract
:1. Introduction
2. Preliminaries
- is nondecreasing,
- for each sequence if ,
- there exist and such that .
- is continuous on instead of the axiom .
3. Absolute Results
- is α-admissible map with respect to ,
- is an -contraction,
- there exists such that ,
- is an -continuous.
- is α-admissible map with respect to ,
- is an -contraction,
- There exists such that ,
- if is an -sequence in such that with as , then, either or holds for all .
4. Application
- There exists a map such that for all with , we have for all ,
- There exists such that for all , ,
- For all and for all and imply ,
- For all and for all .
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Liu, X.; Nallaselli, G.; Haq, A.U.; Gnanaprakasam, A.J.; Baloch, I.A. Fixed Point Results via Orthogonal (α − 𝔶 − 𝔾)-Contraction in Orthogonal Complete Metric Space. Symmetry 2023, 15, 1762. https://doi.org/10.3390/sym15091762
Liu X, Nallaselli G, Haq AU, Gnanaprakasam AJ, Baloch IA. Fixed Point Results via Orthogonal (α − 𝔶 − 𝔾)-Contraction in Orthogonal Complete Metric Space. Symmetry. 2023; 15(9):1762. https://doi.org/10.3390/sym15091762
Chicago/Turabian StyleLiu, Xiaolan, Gunasekaran Nallaselli, Absar Ul Haq, Arul Joseph Gnanaprakasam, and Imran Abbas Baloch. 2023. "Fixed Point Results via Orthogonal (α − 𝔶 − 𝔾)-Contraction in Orthogonal Complete Metric Space" Symmetry 15, no. 9: 1762. https://doi.org/10.3390/sym15091762