Global Optimization and Common Best Proximity Points for Some Multivalued Contractive Pairs of Mappings
Abstract
:1. Preliminaries
- 1.
- In the metric space , is a fixed point of Γ if and only if . In general, if and only if for any .
- 2.
- For two closed sets , when , we have . In that case, a fixed point and a BPP are identical.
- 3.
- The function Δ is continuous in the sense that if as , then as for any .
- 4.
- A CBPP is an element at which the functions and achieve a global minimum, for and for all .
- 1.
- for any and ;
- 2.
- for any .
2. Common Best Proximity Point for MVBCP
3. Common Best Proximity Point for MVKCP
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Debnath, P.; Srivastava, H.M. Global Optimization and Common Best Proximity Points for Some Multivalued Contractive Pairs of Mappings. Axioms 2020, 9, 102. https://doi.org/10.3390/axioms9030102
Debnath P, Srivastava HM. Global Optimization and Common Best Proximity Points for Some Multivalued Contractive Pairs of Mappings. Axioms. 2020; 9(3):102. https://doi.org/10.3390/axioms9030102
Chicago/Turabian StyleDebnath, Pradip, and Hari Mohan Srivastava. 2020. "Global Optimization and Common Best Proximity Points for Some Multivalued Contractive Pairs of Mappings" Axioms 9, no. 3: 102. https://doi.org/10.3390/axioms9030102