Journal of the Iranian Mathematical Society

Journal of the Iranian Mathematical Society

Best proximity point results for generalized multivalued Geraghty-type $\mathcal{F}$- contraction

Articles in Press

Document Type : Research Article

Authors
P. lo$'$lo$'$ 1
M. R. Heidari Tavani 2
M. Shamsizadeh 3
1 Department of Mathematics, Behbahan Khatam Alanbia University of Technology, Behbahan, Iran
2 Department of Mathematics , Ramhormoz Branch, Islamic Azad University, Ramhormoz, Iran
3 Department of Mathematics, Behbahan Khatam Alanbia University of Technology, Behbahan, Iran.
10.30504/jims.2026.575408.1323
Abstract
In this work, we define the concept of generalized multivalued $\mathcal{F}$-contraction for two multivalued non-self-mappings and we prove the existence of a common best proximity point for such multivalued non-self-mappings in complete metric spaces. Then, we provide some interesting results and examples to illustrate our main theorem. We generalize the concept of Geraghty contraction and define generalized multivalued Geraghty-type $\mathcal{F}$-contraction. Finally, as a result of the main theorem, we prove that if a pair of multivalued non-self-mappings apply in such a contraction, then they will have a common best proximity point.
Keywords
Common best proximity
Generalized multivalued $\mathcal{F}$- contraction
Weak property
Geraghty-type $\mathcal{F}$- contraction
Journal of the Iranian Mathematical Society

Articles in Press, Accepted Manuscript
Available Online from 13 October 2026